+
    LV-j	? ã                   óB  € ^ RI t ^ RIHt ^ RIHtHt ^ RIt^ RIt^ RIt	^ RI
Ht ^ RIHt ^ RIHtHtHt ^ RIHt ^ RIHt ^ R	IHt ^ RIHt ^ RIHu Ht ^ R
IHt ^ RIH u H!t" ^ RI#H$t$ ^RI%H&t& ^RI'H(t)H*t+ ^RI,H-t-H.t.H/t/H0t0H1t1H2t2H3t3H4t4H5t5 ^RI6H7t7H8t8H9t9 ^RI:H;t;H<t<H=t=H>t>H?t?H@t@HAtAHBtB ^RICHDtD ^ RIEHFtF ^ RIGHHtH ^ RIIHJtJ R tKR tLERƒR ltM ! R R]14      tN]N! RRRR7      tO ! R R]14      tP]P! ^ RRRR 7      tQ ! R! R"]14      tR]R! RR#R$7      tS]	P¨                  ! ^]	Pª                  ,          4      tV]	P®                  ! ]V4      tXR% tYR& tZR' t[R( t\R) t]R* t^R+ t_R, t` ! R- R.]14      ta]a! R/R07      tb ! R1 R2]14      tc]c! RR3R$7      td ! R4 R5]14      te]e! ]	Pª                  ) ^,          ]	Pª                  ^,          R6R7      tf ! R7 R8]14      tg]g! RRR9R7      th ! R: R;]i4      tj ! R< R=]H4      tkR> tlR? tm ! R@ RA]14      tn]n! RRRBR7      to ! RC RD]14      tp]p! RRER$7      tq ! RF RG]14      tr]r! RRRHR7      ts ! RI RJ]14      tt]t! RRKR$7      tu ! RL RM]14      tv]v! RRNR$7      tw ! RO RP]t4      tx]x! RRQR$7      ty ! RR RS]14      tz]z! RTR07      t{ ! RU RV]14      t|]|! RRWR$7      t} ! RX RY]14      t~]~! RRZR$7      t ! R[ R\]14      t€]€! ]	Pª                  ) ]	Pª                  R]R7      t� ! R^ R_]14      t‚]‚! R`R07      tƒ ! Ra Rb]14      t„]„! ^ RcR$7      t… ! Rd Re]14      t†]†! RfR07      t‡ ! Rg Rh]14      tˆ]ˆ! RRiR$7      t‰ ! Rj Rk]14      tŠ]Š! RlR07      t‹Rm tŒ ! Rn Ro]14      t�]�! RRpR$7      tŽ ! Rq Rr]14      t�]�! RRsR$7      t� ! Rt Ru]14      t‘]‘! RRvR$7      t’ ! Rw Rx]14      t“]“! RRyR$7      t” ! Rz R{]14      t•]•! RR|R$7      t– ! R} R~]14      t—]—! RRR$7      t˜ ! R€ R�]14      t™]™! RR‚R$7      tš ! Rƒ R„]14      t›]›! R…R07      tœER„]œn�         ! R† R‡]14      tž]ž! RRˆR‰7      tŸ ! RŠ R‹]14      t ] ! RŒR07      t¡ ! R� RŽ]14      t¢]¢! RR�R$7      t£ ! R� R‘]14      t¤]¤! RR’R$7      t¥ ! R“ R”]14      t¦]¦! R•R07      t§R– t¨ ! R— R˜]14      t©]©! RR™R$7      tª ! Rš R›]©4      t«]«! RRœR$7      t¬ ! R� Rž]14      t­]­! RRŸR$7      t® ! R  R¡]14      t¯]¯! RR¢R$7      t° ! R£ R¤]14      t±]±! R¥R07      t² ! R¦ R§]14      t³]³! RR¨R$7      t´R© tµ ! Rª R«]14      t¶]¶! R¬R07      t· ! R­ R®]14      t¸]¸! R¯R07      t¹ ! R° R±]14      tº]º! RR²R$7      t» ! R³ R´]14      t¼]¼! RRµR$7      t½ ! R¶ R·]14      t¾]¾! RR¸R$7      t¿ ! R¹ Rº]14      tÀ]À! R»R07      tÁ ! R¼ R½]14      tÂ]Â! RRR¾R7      tÃ ! R¿ RÀ]14      tÄ]Ä! RRÁR$7      tÅ ! RÂ RÃ]14      tÆ]Æ! RRÄR$7      tÇ ! RÅ RÆ]14      tÈ]È! RRÇR$7      tÉ ! RÈ RÉ]14      tÊ]Ê! RÊR07      tË ! RË RÌ]14      tÌ]Ì! ^ RÍR$7      tÍ ! RÎ RÏ]14      tÎ]Î! RÐR07      tÏ ! RÑ RÒ]14      tÐ]Ð! RRRÓR7      tÑ ! RÔ RÕ]14      tÒ]Ò! RÖR07      tÓ ! R× RØ]14      tÔ]Ô! RÙR07      tÕ ! RÚ RÛ]14      tÖ]Ö! RÜR07      t× ! RÝ RÞ]14      tØ]Ø! RßR07      tÙRà tÚ ! Rá Râ]14      tÛ]Û! RRãR$7      tÜ ! Rä Rå]14      tÝ]Ý! RRæR‰7      tÞ ! Rç Rè]14      tß]ß! RéR07      tà ! Rê Rë]14      tá]á! RìR07      tâ ! Rí Rî]14      tã]ã! RRïR$7      täRð tå ! Rñ Rò]14      tæ]æ! RRóR$7      tç ! Rô Rõ]14      tè]è! RRöR$7      té ! R÷ Rø]14      tê]ê! RRùR$7      të ! Rú Rû]14      tì]ì! RRüR$7      tí ! Rý Rþ]14      tî]î! RÿR07      tï ! ER  ER]14      tð]ð! RERR$7      tñ ! ER ER]14      tò]ò! ERR07      tó ! ER ER]14      tô]ô! RERR$7      tõER	 tö ! ER
 ER]14      t÷]÷! RERR$7      tø ! ER ER]14      tù]ù! RERR$7      tú ! ER ER]14      tû]û! ERR07      tü ! ER ER]14      tý]ý! ERR07      tþ ! ER ER]14      tÿ]ÿ! RERR$7      Et  ! ER ER]14      EtE]! RERR$7      Et ! ER ER]14      EtE]! ERR07      Et ! ER ER ]14      EtE]! RRER!R7      Et ! ER" ER#]14      EtE]! RER$R$7      Et ! ER% ER&]14      Et	E]	! ER'R07      Et
 ! ER( ER)]14      EtE]! ER…RER*R7      Et ! ER+ ER,]14      EtE]! RER-R$7      Et ! ER. ER/]14      EtE]! ER0R07      EtE]! ER1R07      EtER„E]n�        ER„E]n�         ! ER2 ER3]14      EtE]! RER4R$7      Et ! ER5 ER6]14      EtE]! ER7R07      EtER†E]n�         ! ER8 ER9]14      EtE]! RER:R$7      Et ! ER; ER<]14      EtE]! ER…RER=R7      Et ! ER> ER?]14      EtE]! ER@R07      Et ! ERA ERB]14      EtE]! ERCR07      Et ! ERD ERE]14      EtE]! RRERFR7      Et ! ERG ERH]14      Et E] ! RRERIR7      Et! ! ERJ ERK]14      Et"E]"! RERLR$7      Et#ER‡E]#n�        ERM Et$ERN Et%ERO Et& ! ERP ERQ]14      Et'E]'! ERR^ERS7      Et(ER„E](n�         ! ERT ERU]14      Et)E])! RERVR$7      Et*ERˆE]*n�         ! ERW ERX]14      Et+E]+! ERYR07      Et, ! ERZ ER[]j4      Et- ! ER\ ER]]14      Et.E].! RRER^R7      Et/ ! ER_ ER`]14      Et0E]0! ERaR07      Et1E]0! ]	Pª                  ) ]	Pª                  ERbR7      Et2 ! ERc ERd]Æ4      Et3E]3! REReR$7      Et4 ! ERf ERg]14      Et5E]5! R^]	Pª                  ,          ERhR7      Et6 ! ERi ERj]14      Et7E]7! ERkR07      Et8 ! ERl ERm]14      Et9E]9! ^ ERnR$7      Et: ! ERo ERp]14      Et;E];! ERqERrERs7      Et<ERt Et= ! ERu ERv]14      Et>E]>! ERwERxRRERy7      Et? ! ERz ER{]14      Et@ ! ER| ER}]14      EtAE]A! ER~^ ]	EP„                  ER7      EtC ! ER€ ER�]14      EtDE]D! RER‚R$7      EtEE]F! E]G! 4       EP‘                  4       EP“                  4       4      EtJ].! E]J]14      w  EtKEtLE]KE]L,           ER{.,           EtMR# (‰  é    N)ÚIterable)ÚwrapsÚcached_property©Ú
Polynomial)ÚBSpline)Úextend_notes_in_docstringÚreplace_notes_in_docstringÚinherit_docstring_from)ÚLowLevelCallable)Úoptimize)Ú	integrate©Ú_lazyselect)Ú
xp_promote)Ú_stats)Útukeylambda_varianceÚtukeylambda_kurtosis)	Ú_vectorize_rvs_over_shapesÚget_distribution_namesÚ	_kurtosisÚ_isintegralÚrv_continuousÚ_skewÚ_get_fixed_fit_valueÚ_check_shapeÚ
_ShapeInfo)ÚkolmognÚkolmognpÚkolmogni)Ú_XMINÚ_LOGXMINÚ_EULERÚ_ZETA3Ú_SQRT_PIÚ_SQRT_2_OVER_PIÚ_LOG_PIÚ_LOG_SQRT_2_OVER_PI)ÚCensoredData)Úroot_scalar)ÚFitErrorc                óÄ   € V P                  RR4       V P                  RR4       V P                  RR4       V P                  RR4       V '       d   \        RV  R24      hR# )aj  
Remove the optimizer-related keyword arguments 'loc', 'scale' and
'optimizer' from `kwds`.  Then check that `kwds` is empty, and
raise `TypeError("Unknown arguments: %s." % kwds)` if it is not.

This function is used in the fit method of distributions that override
the default method and do not use the default optimization code.

`kwds` is modified in-place.
ÚlocNÚscaleÚ	optimizerÚmethodzUnknown arguments: Ú.)ÚpopÚ	TypeError)Úkwdss   &Úo/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/stats/_continuous_distns.pyÚ_remove_optimizer_parametersr6   )   sY   € ð 	‡H�HˆU�DÔØ‡H�HˆW�dÔØ‡H�Hˆ[˜$ÔØ‡H�HˆX�tÔßÜÐ-¨d¨V°1Ð5Ó6Ð6ñ ó    c                 ó0   a € \        S 4      V 3R  l4       pV# )c                 ó&  <€ VP                  R R4      P                  4       p\        V\        4      pVR8X  g   V'       d3   VP	                  4       ^ 8”  d   \
        \        V 4      V `  ! V.VO5/ VB # V'       d   VP                  pS! W.VO5/ VB # )r0   ÚmleÚmm)	ÚgetÚlowerÚ
isinstancer)   Únum_censoredÚsuperÚtypeÚfitÚ_uncensored)ÚselfÚdataÚargsr4   r0   ÚcensoredÚfuns   &&*,  €r5   ÚwrapperÚ _call_super_mom.<locals>.wrapper@   s†   ø€ à—‘˜( EÓ*×0Ñ0Ó2ˆÜ˜d¤LÓ1ˆØ�TŒ>Ÿh¨4×+<Ñ+<Ó+>ÀÔ+BÜœ˜d› TÒ.¨tÐC°dÒC¸dÑCÐCçð ×'Ñ'�Ù�tÐ1 DÒ1¨DÑ1Ð1r7   )r   )rH   rI   s   f r5   Ú_call_super_momrK   <   s"   ø€ ô ˆ3ƒZô2ó ð2ð €Nr7   c                 óÞ   a € T;'       g
    V^,
          pW,
          pV 3R lpV! W!4      '       g=   V^,          pW,
          pRp\         P                  ! V4      '       g   K?  \        V4      hV# )é   c                 óv   <€ \         P                  ! S! V 4      4      \         P                  ! S! V4      4      8g  # ©N©ÚnpÚsign)ÚlbrackÚrbrackrH   s   &&€r5   Úinterval_contains_rootÚ1_get_left_bracket.<locals>.interval_contains_rootX   s(   ø€ ä�wŠw‘s˜6“{Ó#¤r§w¢w©s°6«{Ó';Ñ;Ð;r7   zVThe solver could not find a bracket containing a root to an MLE first order condition.)rQ   ÚisinfÚFitSolverError)rH   rT   rS   ÚdiffrU   Úmsgs   f&&   r5   Ú_get_left_bracketr[   Q   sc   ø€ à×!Ð!�v •z€FØ�?€Dõ<ñ % V×4Ò4Ø��	ˆØ•ˆð7ˆä�8Š8�F×ÔÜ  Ó%Ð%à€Mr7   c                   óN   a € ] tR t^ht o RtR tR tR tR tR t	R t
R tR	tV tR
# )Ú	ksone_gena!  Kolmogorov-Smirnov one-sided test statistic distribution.

This is the distribution of the one-sided Kolmogorov-Smirnov (KS)
statistics :math:`D_n^+` and :math:`D_n^-`
for a finite sample size ``n >= 1`` (the shape parameter).

%(before_notes)s

See Also
--------
kstwobign, kstwo, kstest

Notes
-----
:math:`D_n^+` and :math:`D_n^-` are given by

.. math::

    D_n^+ &= \text{sup}_x (F_n(x) - F(x)),\\
    D_n^- &= \text{sup}_x (F(x) - F_n(x)),\\

where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
`ksone` describes the distribution under the null hypothesis of the KS test
that the empirical CDF corresponds to :math:`n` i.i.d. random variates
with CDF :math:`F`.

%(after_notes)s

References
----------
.. [1] Birnbaum, Z. W. and Tingey, F.H. "One-sided confidence contours
   for probability distribution functions", The Annals of Mathematical
   Statistics, 22(4), pp 592-596 (1951).

Examples
--------
>>> import numpy as np
>>> from scipy.stats import ksone
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Display the probability density function (``pdf``):

>>> n = 1e+03
>>> x = np.linspace(ksone.ppf(0.01, n),
...                 ksone.ppf(0.99, n), 100)
>>> ax.plot(x, ksone.pdf(x, n),
...         'r-', lw=5, alpha=0.6, label='ksone pdf')

Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = ksone(n)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = ksone.ppf([0.001, 0.5, 0.999], n)
>>> np.allclose([0.001, 0.5, 0.999], ksone.cdf(vals, n))
True

c                óH   € V^8¬  V\         P                  ! V4      8H  ,          # ©rM   ©rQ   Úround©rD   Úns   &&r5   Ú	_argcheckÚksone_gen._argcheck¬   ó   € Ø�Q‘˜1¤§¢¨£Ñ+Õ,Ð,r7   c                ó@   € \        R R^\        P                  3R4      .# ©rc   T©TF©r   rQ   Úinf©rD   s   &r5   Ú_shape_infoÚksone_gen._shape_info¯   ó   € Ü˜3  q¬"¯&©& k°=ÓAÐBÐBr7   c                ó0   € \         P                  ! W!4      ) # rO   )ÚscuÚ	_smirnovp©rD   Úxrc   s   &&&r5   Ú_pdfÚksone_gen._pdf²   s   € Ü—’˜aÓ#Ð#Ð#r7   c                ó.   € \         P                  ! W!4      # rO   )rq   Ú	_smirnovcrs   s   &&&r5   Ú_cdfÚksone_gen._cdfµ   s   € Ü�}Š}˜QÓ"Ð"r7   c                ó.   € \         P                  ! W!4      # rO   )ÚscÚsmirnovrs   s   &&&r5   Ú_sfÚksone_gen._sf¸   s   € Ü�zŠz˜!ÓÐr7   c                ó.   € \         P                  ! W!4      # rO   )rq   Ú
_smirnovci©rD   Úqrc   s   &&&r5   Ú_ppfÚksone_gen._ppf»   s   € Ü�~Š~˜aÓ#Ð#r7   c                ó.   € \         P                  ! W!4      # rO   )r|   Úsmirnovir‚   s   &&&r5   Ú_isfÚksone_gen._isf¾   ó   € Ü�{Š{˜1Ó Ð r7   © N)Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__doc__rd   rm   ru   ry   r~   r„   rˆ   Ú__static_attributes__Ú__classdictcell__©Ú__classdict__s   @r5   r]   r]   h   s5   ø‡ € ñBòF-òCò$ò#ò ò$÷!ð !r7   r]   ç        ç      ð?Úksone)ÚaÚbÚnamec                   óT   a € ] tR t^Åt o RtR tR tR tR tR t	R t
R tR	 tR
tV tR# )Ú	kstwo_gena¨  Kolmogorov-Smirnov two-sided test statistic distribution.

This is the distribution of the two-sided Kolmogorov-Smirnov (KS)
statistic :math:`D_n` for a finite sample size ``n >= 1``
(the shape parameter).

%(before_notes)s

See Also
--------
kstwobign, ksone, kstest

Notes
-----
:math:`D_n` is given by

.. math::

    D_n = \text{sup}_x |F_n(x) - F(x)|

where :math:`F` is a (continuous) CDF and :math:`F_n` is an empirical CDF.
`kstwo` describes the distribution under the null hypothesis of the KS test
that the empirical CDF corresponds to :math:`n` i.i.d. random variates
with CDF :math:`F`.

%(after_notes)s

References
----------
.. [1] Simard, R., L'Ecuyer, P. "Computing the Two-Sided
   Kolmogorov-Smirnov Distribution",  Journal of Statistical Software,
   Vol 39, 11, 1-18 (2011).

Examples
--------
>>> import numpy as np
>>> from scipy.stats import kstwo
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Display the probability density function (``pdf``):

>>> n = 10
>>> x = np.linspace(kstwo.ppf(0.01, n),
...                 kstwo.ppf(0.99, n), 100)
>>> ax.plot(x, kstwo.pdf(x, n),
...         'r-', lw=5, alpha=0.6, label='kstwo pdf')

Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = kstwo(n)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = kstwo.ppf([0.001, 0.5, 0.999], n)
>>> np.allclose([0.001, 0.5, 0.999], kstwo.cdf(vals, n))
True

c                óH   € V^8¬  V\         P                  ! V4      8H  ,          # r_   r`   rb   s   &&r5   rd   Úkstwo_gen._argcheck  rf   r7   c                ó@   € \        R R^\        P                  3R4      .# rh   rj   rl   s   &r5   rm   Úkstwo_gen._shape_info  ro   r7   c                ó€   € R \        V\        4      '       g   V,          R3# \        P                  ! V4      ,          R3# ©ç      à?r–   )r>   r   rQ   Ú
asanyarrayrb   s   &&r5   Ú_get_supportÚkstwo_gen._get_support  s>   € Øœj¨¬H×5Ò5�QÕLØðð 	¼2¿=º=ÈÓ;KÕLØðð 	r7   c                ó   € \        W!4      # rO   )r   rs   s   &&&r5   ru   Úkstwo_gen._pdf  s   € Ü˜‹~Ðr7   c                ó   € \        W!4      # rO   ©r   rs   s   &&&r5   ry   Úkstwo_gen._cdf  s   € Ü�q‹}Ðr7   c                ó   € \        W!R R7      # ©F©Úcdfrª   rs   s   &&&r5   r~   Úkstwo_gen._sf  s   € Ü�q Ô'Ð'r7   c                ó   € \        W!R R7      # )Tr®   ©r    r‚   s   &&&r5   r„   Úkstwo_gen._ppf  s   € Ü˜ $Ô'Ð'r7   c                ó   € \        W!R R7      # r­   r²   r‚   s   &&&r5   rˆ   Úkstwo_gen._isf  s   € Ü˜ %Ô(Ð(r7   r‹   N)rŒ   r�   rŽ   r�   r�   rd   rm   r¥   ru   ry   r~   r„   rˆ   r‘   r’   r“   s   @r5   rœ   rœ   Å   s:   ø‡ € ñAòD-òCòòòò(ò(÷)ð )r7   rœ   Úkstwo)Úmomtyper˜   r™   rš   c                   óH   a € ] tR tRt o RtR tR tR tR tR t	R t
R	tV tR
# )Úkstwobign_geni&  a¨  Limiting distribution of scaled Kolmogorov-Smirnov two-sided test statistic.

This is the asymptotic distribution of the two-sided Kolmogorov-Smirnov
statistic :math:`\sqrt{n} D_n` that measures the maximum absolute
distance of the theoretical (continuous) CDF from the empirical CDF.
(see `kstest`).

%(before_notes)s

See Also
--------
ksone, kstwo, kstest

Notes
-----
:math:`\sqrt{n} D_n` is given by

.. math::

    D_n = \text{sup}_x |F_n(x) - F(x)|

where :math:`F` is a continuous CDF and :math:`F_n` is an empirical CDF.
`kstwobign`  describes the asymptotic distribution (i.e. the limit of
:math:`\sqrt{n} D_n`) under the null hypothesis of the KS test that the
empirical CDF corresponds to i.i.d. random variates with CDF :math:`F`.

%(after_notes)s

References
----------
.. [1] Feller, W. "On the Kolmogorov-Smirnov Limit Theorems for Empirical
   Distributions",  Ann. Math. Statist. Vol 19, 177-189 (1948).

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úkstwobign_gen._shape_infoK  ó   € Øˆ	r7   c                ó0   € \         P                  ! V4      ) # rO   )rq   Ú_kolmogp©rD   rt   s   &&r5   ru   Úkstwobign_gen._pdfN  s   € Ü—’˜Q“ÐÐr7   c                ó.   € \         P                  ! V4      # rO   )rq   Ú_kolmogcr¿   s   &&r5   ry   Úkstwobign_gen._cdfQ  s   € Ü�|Š|˜A‹Ðr7   c                ó.   € \         P                  ! V4      # rO   )r|   Ú
kolmogorovr¿   s   &&r5   r~   Úkstwobign_gen._sfT  s   € Ü�}Š}˜QÓÐr7   c                ó.   € \         P                  ! V4      # rO   )rq   Ú	_kolmogci©rD   rƒ   s   &&r5   r„   Úkstwobign_gen._ppfW  s   € Ü�}Š}˜QÓÐr7   c                ó.   € \         P                  ! V4      # rO   )r|   ÚkolmogirÉ   s   &&r5   rˆ   Úkstwobign_gen._isfZ  s   € Ü�zŠz˜!‹}Ðr7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   ry   r~   r„   rˆ   r‘   r’   r“   s   @r5   r¹   r¹   &  s.   ø‡ € ñ#òHò òò ò ÷ð r7   r¹   Ú	kstwobign)r˜   rš   c                 ób   € \         P                  ! V ^,          ) R,          4      \        ,          # ©é   ç       @)rQ   ÚexpÚ_norm_pdf_C©rt   s   &r5   Ú	_norm_pdfrÖ   j  s    € Ü�6Š6�1�a•4�%˜•)Óœ{Õ*Ð*r7   c                 ó:   € V ^,          ) R,          \         ,
          # rÐ   )Ú_norm_pdf_logCrÕ   s   &r5   Ú_norm_logpdfrÙ   n  s   € Øˆq�Dˆ5�3�;œÕ'Ð'r7   c                 ó.   € \         P                  ! V 4      # rO   )r|   ÚndtrrÕ   s   &r5   Ú	_norm_cdfrÜ   r  s   € Ü�7Š7�1‹:Ðr7   c                 ó.   € \         P                  ! V 4      # rO   )r|   Úlog_ndtrrÕ   s   &r5   Ú_norm_logcdfrß   v  s   € Ü�;Š;�q‹>Ðr7   c                 ó.   € \         P                  ! V 4      # rO   )r|   Úndtri©rƒ   s   &r5   Ú	_norm_ppfrã   z  s   € Ü�8Š8�A‹;Ðr7   c                 ó   € \        V ) 4      # rO   ©rÜ   rÕ   s   &r5   Ú_norm_sfræ   ~  s   € Ü�a�R‹=Ðr7   c                 ó   € \        V ) 4      # rO   ©rß   rÕ   s   &r5   Ú_norm_logsfré   ‚  s   € Ü˜˜ÓÐr7   c                 ó   € \        V 4      ) # rO   ©rã   râ   s   &r5   Ú	_norm_isfrì   †  s   € Ü�a‹Lˆ=Ðr7   c                   ó    a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tR tR t]]! ]RR7      R 4       4       tR tRtV tR# )Únorm_geniŠ  a]  A normal continuous random variable.

The location (``loc``) keyword specifies the mean.
The scale (``scale``) keyword specifies the standard deviation.

%(before_notes)s

Notes
-----
The probability density function for `norm` is:

.. math::

    f(x) = \frac{\exp(-x^2/2)}{\sqrt{2\pi}}

for a real number :math:`x`.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Únorm_gen._shape_info¡  r¼   r7   Nc                ó$   € VP                  V4      # rO   )Ústandard_normal©rD   ÚsizeÚrandom_states   &&&r5   Ú_rvsÚnorm_gen._rvs¤  s   € Ø×+Ñ+¨DÓ1Ð1r7   c                ó   € \        V4      # rO   ©rÖ   r¿   s   &&r5   ru   Únorm_gen._pdf§  s   € ä˜‹|Ðr7   c                ó   € \        V4      # rO   ©rÙ   r¿   s   &&r5   Ú_logpdfÚnorm_gen._logpdf«  ó   € Ü˜A‹Ðr7   c                ó   € \        V4      # rO   rå   r¿   s   &&r5   ry   Únorm_gen._cdf®  ó   € Ü˜‹|Ðr7   c                ó   € \        V4      # rO   rè   r¿   s   &&r5   Ú_logcdfÚnorm_gen._logcdf±  rÿ   r7   c                ó   € \        V4      # rO   ©ræ   r¿   s   &&r5   r~   Únorm_gen._sf´  s   € Ü˜‹{Ðr7   c                ó   € \        V4      # rO   )ré   r¿   s   &&r5   Ú_logsfÚnorm_gen._logsf·  s   € Ü˜1‹~Ðr7   c                ó   € \        V4      # rO   rë   rÉ   s   &&r5   r„   Únorm_gen._ppfº  r  r7   c                ó   € \        V4      # rO   ©rì   rÉ   s   &&r5   rˆ   Únorm_gen._isf½  r  r7   c                ó   € R# )r•   )r•   r–   r•   r•   r‹   rl   s   &r5   r   Únorm_gen._statsÀ  ó   € Ø!Ð!r7   c                ót   € R \         P                  ! ^\         P                  ,          4      ^,           ,          # ©r£   ©rQ   ÚlogÚpirl   s   &r5   Ú_entropyÚnorm_gen._entropyÃ  s"   € Ø”B—F’F˜1œRŸU™U�7“O AÕ%Õ&Ð&r7   a}          For the normal distribution, method of moments and maximum likelihood
        estimation give identical fits, and explicit formulas for the estimates
        are available.
        This function uses these explicit formulas for the maximum likelihood
        estimation of the normal distribution parameters, so the
        `optimizer` and `method` arguments are ignored.

©Únotesc                óÄ  € VP                  R R4      pVP                  RR4      p\        V4       Ve   Ve   \        R4      h\        P                  ! V4      p\        P
                  ! V4      P                  4       '       g   \        R4      hVf   VP                  4       pMTpVf5   \        P                  ! W,
          ^,          P                  4       4      pWV3# TpWV3# )ÚflocNÚfscaleú3All parameters fixed. There is nothing to optimize.ú$The data contains non-finite values.)	r2   r6   Ú
ValueErrorrQ   ÚasarrayÚisfiniteÚallÚmeanÚsqrt)rD   rE   r4   r  r  r-   r.   s   &&,    r5   rB   Únorm_gen.fitÆ  sÏ   € ð �x‰x˜ Ó%ˆØ—‘˜( DÓ)ˆä$ TÔ*àÒ Ò 2ô ð )ó *ð *ô �zŠz˜$Óˆä�{Š{˜4Ó ×$Ñ$×&Ò&ÜÐCÓDÐDàŠ<Ø—)‘)“+‰CàˆCàŠ>Ü—G’G˜d�j¨1�_×2Ñ2Ó4Ó5ˆEð ˆzÐð ˆEàˆzÐr7   c                ó€   € V^ 8X  d   R# V^,          ^ 8X  d'   \         P                  ! \        V4      ^,
          4      # R# )zv
@returns Moments of standard normal distribution for integer n >= 0

See eq. 16 of https://arxiv.org/abs/1209.4340v2
r–   r•   )r|   Ú
factorial2Úintrb   s   &&r5   Ú_munpÚnorm_gen._munpì  s3   € ð �Œ6ÙØˆq�5�AŒ:Ü—=’=¤ Q£¨!¥Ó,Ð,ár7   r‹   ©NN)rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r  r~   r
  r„   rˆ   r   r  rK   r
   r   rB   r,  r‘   r’   r“   s   @r5   rî   rî   Š  sz   ø‡ € ñò,ô2òòòòòòòòò"ò'ð Ù ð 6?ô @ñó@ó ð÷<ð r7   rî   Únorm)rš   c                   ó`   a € ] tR tRt o Rt]P                  tR tR t	R t
R tR tR tR	tV tR
# )Ú	alpha_geniý  aÖ  An alpha continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `alpha` ([1]_, [2]_) is:

.. math::

    f(x, a) = \frac{1}{x^2 \Phi(a) \sqrt{2\pi}} *
              \exp(-\frac{1}{2} (a-1/x)^2)

where :math:`\Phi` is the normal CDF, :math:`x > 0`, and :math:`a > 0`.

`alpha` takes ``a`` as a shape parameter.

%(after_notes)s

References
----------
.. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
       Distributions, Volume 1", Second Edition, John Wiley and Sons,
       p. 173 (1994).
.. [2] Anthony A. Salvia, "Reliability applications of the Alpha
       Distribution", IEEE Transactions on Reliability, Vol. R-34,
       No. 3, pp. 251-252 (1985).

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# ©r˜   F©FFrj   rl   s   &r5   rm   Úalpha_gen._shape_info  ó   € Ü˜3 ¨¬2¯6©6 {°NÓCÐDÐDr7   c                ó~   € R V^,          ,          \        V4      ,          \        VR V,          ,
          4      ,          # ©r–   )rÜ   rÖ   ©rD   rt   r˜   s   &&&r5   ru   Úalpha_gen._pdf"  s+   € à�A�q•D�zœ) A›,Õ&¤y°°3°qµ5µÓ'9Õ9Ð9r7   c                óÀ   € R\         P                  ! V4      ,          \        VRV,          ,
          4      ,           \         P                  ! \        V4      4      ,
          # )rÑ   r–   éþÿÿÿ)rQ   r  rÙ   rÜ   r9  s   &&&r5   rý   Úalpha_gen._logpdf&  s8   € Ø”"—&’&˜“)�|œl¨1¨S°­U­7Ó3Õ3´b·f²f¼YÀq»\Ó6JÕJÐJr7   c                óT   € \        VR V,          ,
          4      \        V4      ,          # r8  rå   r9  s   &&&r5   ry   Úalpha_gen._cdf)  s   € Ü˜˜3˜q�5�Ó!¤I¨a£LÕ0Ð0r7   c           
     ó|   € R \         P                  ! V\        V\        V4      ,          4      ,
          4      ,          # r8  )rQ   r#  rã   rÜ   ©rD   rƒ   r˜   s   &&&r5   r„   Úalpha_gen._ppf,  s(   € Ø”2—:’:˜a¤)¨A¬i¸«l­NÓ";Õ;Ó<Õ<Ð<r7   c                ól   € \         P                  .^,          \         P                  .^,          ,           # ©rÑ   ©rQ   rk   Únan©rD   r˜   s   &&r5   r   Úalpha_gen._stats/  s!   € Ü—‘ˆx˜�zœRŸV™V˜H Q�JÕ&Ð&r7   r‹   N)rŒ   r�   rŽ   r�   r�   r   Ú_open_support_maskÚ_support_maskrm   ru   rý   ry   r„   r   r‘   r’   r“   s   @r5   r1  r1  ý  s<   ø‡ € ñð> "×4Ñ4€MòEò:òKò1ò=÷'ð 'r7   r1  Úalphac                   óN   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
tV tR# )Ú
anglit_geni6  zîAn anglit continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `anglit` is:

.. math::

    f(x) = \sin(2x + \pi/2) = \cos(2x)

for :math:`-\pi/4 \le x \le \pi/4`.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úanglit_gen._shape_infoJ  r¼   r7   c                ó<   € \         P                  ! ^V,          4      # rD  )rQ   Úcosr¿   s   &&r5   ru   Úanglit_gen._pdfM  s   € ä�vŠv�a˜•c‹{Ðr7   c                ót   € \         P                  ! V\         P                  ^,          ,           4      R,          # ©é   rÒ   ©rQ   Úsinr  r¿   s   &&r5   ry   Úanglit_gen._cdfQ  s"   € Ü�vŠv�aœŸ™˜a�•iÓ  #Õ%Ð%r7   c                ót   € \         P                  ! V\         P                  ^,          ,           4      R,          # rT  )rQ   rQ  r  r¿   s   &&r5   r~   Úanglit_gen._sfT  s"   € Ü�vŠv�aœ"Ÿ%™% !�)•mÓ$¨Õ+Ð+r7   c                óŽ   € \         P                  ! \         P                  ! V4      4      \         P                  ^,          ,
          # ©rU  )rQ   Úarcsinr'  r  rÉ   s   &&r5   r„   Úanglit_gen._ppfW  s&   € Ü�yŠyœŸš ›Ó$¤R§U¡U¨1¥WÕ,Ð,r7   c                ó&  € R \         P                  \         P                  ,          ^,          R,
          R R\         P                  ^,          ^`,
          ,          \         P                  \         P                  ,          ^,
          ^,          ,          3# )r•   r£   r<  ©rQ   r  rl   s   &r5   r   Úanglit_gen._statsZ  sR   € Ø”B—E‘Eœ"Ÿ%™%•K •N 3Õ&¨¨R´·±¸µ¸BµÕ-?ÄÇÁÄrÇuÁuÅÈQÅÐQRÕ@RÕ-RÐRÐRr7   c                ó<   € ^\         P                  ! ^4      ,
          # r_   ©rQ   r  rl   s   &r5   r  Úanglit_gen._entropy]  ó   € Ø”—’˜“�{Ðr7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   ry   r~   r„   r   r  r‘   r’   r“   s   @r5   rM  rM  6  s3   ø‡ € ñò&òò&ò,ò-òS÷ð r7   rM  Úanglitc                   óH   a € ] tR tRt o RtR tR tR tR tR t	R t
R	tV tR
# )Úarcsine_genid  zäAn arcsine continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `arcsine` is:

.. math::

    f(x) = \frac{1}{\pi \sqrt{x (1-x)}}

for :math:`0 < x < 1`.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úarcsine_gen._shape_infox  r¼   r7   c                óþ   € \         P                  ! R R7      ;_uu_ 4        R\         P                  ,          \         P                  ! V^V,
          ,          4      ,          uuRRR4       #   + '       g   i     R# ; i)Úignore©Údivider–   N)rQ   Úerrstater  r'  r¿   s   &&r5   ru   Úarcsine_gen._pdf{  sA   € ä�[Š[ ×)Ö)Ø”r—u‘u•9œRŸWšW Q¨¨!­¥WÓ-Õ-÷ *×)×)Ó)ús    A A+Á+A<	c                óŽ   € R \         P                  ,          \         P                  ! \         P                  ! V4      4      ,          # ©rÒ   )rQ   r  r]  r'  r¿   s   &&r5   ry   Úarcsine_gen._cdf€  s&   € Ø”2—5‘5�yœŸš¤2§7¢7¨1£:Ó.Õ.Ð.r7   c                ót   € \         P                  ! \         P                  R ,          V,          4      R ,          # rr  rV  rÉ   s   &&r5   r„   Úarcsine_gen._ppfƒ  s"   € Ü�vŠv”b—e‘e˜C•i •kÓ" CÕ'Ð'r7   c                ó   € R pRp^ pRpWW43# )r£   g      À?ç      ø¿r‹   ©rD   ÚmuÚmu2Úg1Úg2s   &    r5   r   Úarcsine_gen._stats†  s    € ØˆØˆØˆØˆØ˜ˆÐr7   c                ó   € R# )g‘Á”°•ëÎ?g‘Á”°•ëÎ¿r‹   rl   s   &r5   r  Úarcsine_gen._entropy�  s   € Ø&Ð&r7   r‹   N©rŒ   r�   rŽ   r�   r�   rm   ru   ry   r„   r   r  r‘   r’   r“   s   @r5   rh  rh  d  s-   ø‡ € ñò&ò.ò
/ò(ò÷'ð 'r7   rh  Úarcsinec                   ó*   a € ] tR tRt o RtR tRtV tR# )ÚFitDataErrori”  z=Raised when input data is inconsistent with fixed parameters.c                ó0   € R V: RV: RV: R23V n         R# )z>Invalid values in `data`.  Maximum likelihood estimation with z requires that z < (x - loc)/scale  < z for each x in `data`.N©rF   )rD   Údistrr=   Úuppers   &&&&r5   Ú__init__ÚFitDataError.__init__™  s/   € ðØ$™i °u±ið @"Ø"'¡Ð*@ðBð
ˆŽ	r7   r…  N©rŒ   r�   rŽ   r�   r�   rˆ  r‘   r’   r“   s   @r5   rƒ  rƒ  ”  s   ø‡ € ÙG÷
ð 
r7   rƒ  c                   ó*   a € ] tR tRt o RtR tRtV tR# )rX   i¡  zF
Raised when a solver fails to converge while fitting a distribution.
c                óJ   € R pW!P                  RR4      ,          pV3V n        R# )z1Solver for the MLE equations failed to converge: Ú
Ú N)ÚreplacerF   )rD   ÚmesgÚemsgs   && r5   rˆ  ÚFitSolverError.__init__§  s#   € ØBˆØ—‘˜T 2Ó&Õ&ˆØ�GˆŽ	r7   r…  NrŠ  r“   s   @r5   rX   rX   ¡  s   ø‡ € ñ÷
ð r7   rX   c                 ó”   € \         P                  ! W,           4      pW2V) \         P                  ! V 4      ,           ,          ,
          pV# rO   ©r|   Úpsi)r˜   r™   rc   Ús1ÚpsiabÚfuncs   &&&&  r5   Ú_beta_mle_ar™  ­  s4   € ô �FŠF�1•5‹M€EØ�e�VœbŸfšf Q›iÕ'Õ(Õ(€DØ€Kr7   c                 óò   € V w  rE\         P                  ! WE,           4      pW!V) \         P                  ! V4      ,           ,          ,
          W1V) \         P                  ! V4      ,           ,          ,
          .pV# rO   r”  )Úthetarc   r–  Ús2r˜   r™   r—  r˜  s   &&&&    r5   Ú_beta_mle_abr�  ¶  sZ   € ð �D€AÜ�FŠF�1•5‹M€EØ�u�fœrŸvšv a›yÕ(Õ)Õ)Ø�u�fœrŸvšv a›yÕ(Õ)Õ)ð+€Dà€Kr7   c                   ó¦   a a€ ] tR tRt oRtR tRR ltR tR tR t	R t
R	 tR
 tR tV 3R lt]]! ]RR7      V 3R l4       4       tR tRtVtV ;t# )Úbeta_geniÄ  aø  A beta continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `beta` is:

.. math::

    f(x, a, b) = \frac{\Gamma(a+b) x^{a-1} (1-x)^{b-1}}
                      {\Gamma(a) \Gamma(b)}

for :math:`0 <= x <= 1`, :math:`a > 0`, :math:`b > 0`, where
:math:`\Gamma` is the gamma function (`scipy.special.gamma`).

`beta` takes :math:`a` and :math:`b` as shape parameters.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
methods. [1]_

Maximum likelihood estimates of parameters are only available when the location and
scale are fixed. When either of these parameters is free, ``beta.fit`` resorts to
numerical optimization, but this problem is unbounded: the location and scale may be
chosen to make the minimum and maximum elements of the data coincide with the
endpoints of the support, and the shape parameters may be chosen to make the PDF at
these points infinite. For best results, pass ``floc`` and ``fscale`` keyword
arguments to fix the location and scale, or use `scipy.stats.fit` with
``method='mse'``.

%(after_notes)s

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# ©r˜   Fr™   r4  rj   ©rD   ÚiaÚibs   &  r5   rm   Úbeta_gen._shape_infoí  ó9   € Ü˜˜U Q¬¯© K°Ó@ˆÜ˜˜U Q¬¯© K°Ó@ˆØˆxˆr7   c                ó&   € VP                  WV4      # rO   ©Úbeta)rD   r˜   r™   rô   rõ   s   &&&&&r5   rö   Úbeta_gen._rvsò  s   € Ø× Ñ   tÓ,Ð,r7   c                ó¬   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! WV4      uuRRR4       #   + '       g   i     R# ; i©rl  ©ÚoverN)rQ   ro  rq   Ú	_beta_pdf©rD   rt   r˜   r™   s   &&&&r5   ru   Úbeta_gen._pdfõ  s0   € ô �[Š[˜h×'Ö'Ü—=’=  qÓ)÷ (×'×'Ó'úó    AÁA	c                óÄ   € \         P                  ! VR ,
          V) 4      \         P                  ! VR ,
          V4      ,           pV\         P                  ! W#4      ,          pV# r8  )r|   Úxlog1pyÚxlogyÚbetaln)rD   rt   r˜   r™   ÚlPxs   &&&& r5   rý   Úbeta_gen._logpdfü  sC   € Ü�jŠj˜˜S� 1 "Ó%¬¯ª°°Sµ¸!Ó(<Õ<ˆØŒr�yŠy˜‹ÕˆØˆ
r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Úbetaincr°  s   &&&&r5   ry   Úbeta_gen._cdf  s   € Ü�zŠz˜! Ó"Ð"r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Úbetainccr°  s   &&&&r5   r~   Úbeta_gen._sf  s   € Ü�{Š{˜1 Ó#Ð#r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Úbetainccinvr°  s   &&&&r5   rˆ   Úbeta_gen._isf  s   € Ü�~Š~˜a AÓ&Ð&r7   c                ó0   € \         P                  ! WV4      # rO   )rq   Ú	_beta_ppf©rD   rƒ   r˜   r™   s   &&&&r5   r„   Úbeta_gen._ppf
  s   € Ü�}Š}˜Q 1Ó%Ð%r7   c                ó  € W,           pW,          pW,          V^,          V^,           ,          ,          p^W!,
          ,          \         P                  ! V^,           4      ,          V^,           \         P                  ! W,          4      ,          ,          p^W,
          ^,          V^,           ,          W,          V^,           ,          ,
          ,          pW,          V^,           ,          V^,           ,          pWx,          p	VVVV	3# rD  ©rQ   r'  )
rD   r˜   r™   Úa_plus_bÚ
_beta_meanÚ_beta_varianceÚ_beta_skewnessÚ_beta_kurtosis_excess_nÚ_beta_kurtosis_excess_dÚ_beta_kurtosis_excesss
   &&&       r5   r   Úbeta_gen._stats  sÉ   € Ø•5ˆØ•Zˆ
Ø� ¨!¥¨x¸!­|Õ <Õ=ˆØ ¥�;¬¯ª°¸AµÓ)>Õ>Ø$ q�L¬B¯GªG°AµE«NÕ:õ<ˆà"#¨­°¥z°XÀµ\Õ'BØ'(¥u°¸1µÕ'=õ(>õ #?Ðà"#¥%¨8°a­<Õ"8¸HÀq½LÕ"IÐØ 7Õ QÐàØØØ!ð	#ð 	#r7   c                óä   <aa€ \        V\        4      '       d   VP                  4       p\        V4      o\	        V4      oVV3R  lp\
        P                  ! VR4      w  r4\        SV `!  WV3R7      # )c                 ó^  <€ V w  r^W!,
          ,          \         P                  ! W,           ^,           4      ,          W,           ^,           ,          \         P                  ! W,          4      ,          pV^,          V^,          ^V,          ^,
          ,          ,
          V^,          V^,           ,          ,           ^V,          V,          V^,           ,          ,
          pWAV,          W,           ^,           ,          W,           ^,           ,          ,          pV^,          pVS,
          VS,
          .# rD  rÇ  )rt   r˜   r™   ÚskÚkur{  r|  s   &    €€r5   r˜  Ú beta_gen._fitstart.<locals>.func$  sÃ   ø€ Ø‰DˆAØ�A•C•œŸš ¥¨¥Ó+Õ+¨q­u°q­yÕ9¼B¿GºGÀAÅC»LÕHˆBØ�A•˜˜1�˜a �c !�e�Õ$ q¨!¥t¨Q¨q­S¥zÕ1°A°aµC¸µE¸1¸Q½3µKÕ?ˆBØ�A•#�q•s˜1•u•+˜q�s 1�uÕ%Õ%ˆBØ�!�GˆBØ�r•E˜2˜b�5�>Ð!r7   r…  )r–   r–   )	r>   r)   Ú	_uncensorr   r   r   Úfsolver@   Ú	_fitstart)rD   rE   r˜  r˜   r™   r{  r|  Ú	__class__s   &&   @@€r5   r×  Úbeta_gen._fitstart  s^   ú€ Ü�dœL×)Ò)Ø—>‘>Ó#ˆDä�4‹[ˆÜ�t‹_ˆö	"ô �Š˜t ZÓ0‰ˆÜ‰wÑ  °¨FÐ Ó3Ð3r7   zÓ        In the special case where `method="MLE"` and
        both `floc` and `fscale` are given, a
        `ValueError` is raised if any value `x` in `data` does not satisfy
        `floc < x < floc + fscale`.

r  c           	     ó¾  <€ VP                  R R4      pVP                  RR4      pVe   Vf   \        SV `  ! V.VO5/ VB # VP                  R R4       VP                  RR4       \	        V. RO4      p\	        V. RO4      p\        V4       Ve   Ve   \        R4      h\        P                  ! V4      P                  4       '       g   \        R4      h\        P                  ! V4      V,
          V,          p\        P                  ! V^ 8*  4      '       g    \        P                  ! V^8¬  4      '       d   \        RWDV,           R7      hVP                  4       pVf   Ve¤   Ve   Tp	^V,
          p^V,
          pMTp	W˜,          ^V,
          ,          p
\        P                  ! \         V
V	\#        V4      \        P$                  ! V4      P'                  4       3RR7      w  r¼rÞV^8w  d   \)        VR	7      hV^ ,          p
Ve   YšršMÕ\        P$                  ! V4      P'                  4       p\*        P,                  ! V) 4      P'                  4       pV^V,
          ,          VP/                  ^ R
7      ,          ^,
          pVV,          p
^V,
          V,          p	\        P                  ! \0        W©.\#        V4      VV3RR7      w  r¼rÞV^8w  d   \)        VR	7      hVw  r©W©WE3# )r  Nr  r   r!  r©  ©r=   r‡  T)rF   Úfull_output)r�  )Úddof©Úf0ÚfaÚfix_a)Úf1ÚfbÚfix_b)r<   r@   rB   r2   r   r6   r"  rQ   r$  r%  ÚravelÚanyrƒ  r&  r   rÖ  r™  Úlenr  ÚsumrX   r|   Úlog1pÚvarr�  )rD   rE   rF   r4   r  r  rß  râ  Úxbarr™   r˜   r›  ÚinfoÚierr�  r–  rœ  ÚfacrØ  s   &&*,              €r5   rB   Úbeta_gen.fit.  s‡  ø€ ð �x‰x˜ Ó%ˆØ—‘˜( DÓ)ˆàŠ<˜6š>ä‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ð 	�‰�˜ÔØ�‰�˜4Ô ä! $Ò(=Ó>ˆÜ! $Ò(=Ó>ˆä$ TÔ*àŠ>˜bšnäð )ó *ð *ô �{Š{˜4Ó ×$Ñ$×&Ò&ÜÐCÓDÐDô —’˜“ Õ%¨Õ/ˆÜ�6Š6�$˜!‘)×Ò¤§¢ t¨q¡y× 1Ò 1Ü˜v¨TÀ½ÔGÐGà�y‰y‹{ˆàŠ>˜Rš^ð Š~ð �Ø˜4•x�Ø˜4•x‘à�ð •˜A �HÕ%ˆAô &.§_¢_Ü˜QØœ˜T›¤B§F¢F¨4£L×$4Ñ$4Ó$6Ð7Ø ô&Ñ"ˆE˜ð
 �aŒxÜ$¨$Ô/Ð/Ø�a•ˆAàŠ~ð �1øô —’˜“×!Ñ!Ó#ˆBÜ—’˜4˜%“×$Ñ$Ó&ˆBð ˜!˜d�(Õ# d§h¡h°A hÓ&6Õ6¸Õ:ˆCØ�s•
ˆAØ�T•˜SÕ ˆAô &.§_¢_Ü˜q˜fÜ˜$“i  RÐ(Ø ô&Ñ"ˆE˜ð
 �aŒxÜ$¨$Ô/Ð/Ø‰DˆAà�TÐ!Ð!r7   c                ó  a	€ R  pR pR o	V	3R lpR pV! V4      pV! V4      p\        VR8¬  VR8¬  ,          VR8*  W!,
          R8¬  ,          W'8¬  ,          VR8*  W,
          R8¬  ,          W8¬  ,          VR8  VR8  ,          .VS	WS.W.4      # )c                 ó<  € \         P                  ! W4      V ^,
          \         P                  ! V 4      ,          ,
          V^,
          \         P                  ! V4      ,          ,
          W,           ^,
          \         P                  ! W,           4      ,          ,           # r_   )r|   r¶  r•  ©r˜   r™   s   &&r5   ÚregularÚ"beta_gen._entropy.<locals>.regularš  s`   € Ü—I’I˜a“O q¨1¥u´·²°q³	Õ&9Õ9Ø˜•UœbŸfšf Q›iÕ'õ(Ø+,­5°1­9¼¿º¸q½u»Õ*EõFð Gr7   c                 óØ  € W,           pR \         P                  ! ^\         P                  ,          4      \         P                  ! V 4      ,           \         P                  ! V4      ,           ^\         P                  ! V4      ,          ,
          ^,           ,          p^nV,          ^VR,          ,          ,           VR,          ,           ^VR,          ,          ,
          pRV ,          ^
V R,          ,          ,
          V R,          ,
          V R,          ,           pRV,          ^
VR,          ,          ,
          VR,          ,
          VR,          ,           pW4V,           V,           ^x,          ,           # )r£   ç       Àç      Àç      ÀiÎÿÿÿr  )r˜   r™   Úsum_abÚlog_termÚt1Út2Út3s   &&     r5   Úasymptotic_ab_largeÚ.beta_gen._entropy.<locals>.asymptotic_ab_largež  së   € Ø•UˆFØÜ—’�qœŸ™•w“¤"§&¢&¨£)Õ+¬b¯fªf°Q«iÕ7¸!¼B¿FºFÀ6»NÕ:JÕJÈQÕNõˆHð �V•˜b ¨¥�oÕ-°¸µÕ<¸qÀÈÅ½~ÕMˆBØ�Q•˜˜A˜t�G�Õ# a¨¥gÕ-°°4µÕ7ˆBØ�Q•˜˜A˜t�G�Õ# a¨¥gÕ-°°4µÕ7ˆBØ B�w¨�|¨sÕ2Õ2Ð2r7   c                 ó¢  € W,           p\         P                  ! V 4      V ^,
          \         P                  ! V 4      ,          ,
          pR^V,          ,          ^^V,          ,          ,           VR,          ^,          ,
          VR,          ^x,          ,
          VR,          ^x,          ,           VR,          ^ü,          ,           VR,          ^ü,          ,
          ^V,          ,           ^^V,          ,          ,
          VR,          ^,          ,           VR,          ^x,          ,           VR,          ^<,          ,
          VR,          ^ü,          ,
          VR,          ^~,          ,           pV\        P                  ! W,          4      ,          \        P
                  ! V4      ,           ^\        P
                  ! V4      ,          ,
          pW4,           V,           # )rM   éÿÿÿÿrö  r÷  rø  ç      Àç      À)r|   Úgammalnr•  rQ   ré  r  )r˜   r™   rù  rû  rü  rú  s   &&    r5   Úasymptotic_b_largeÚ-beta_gen._entropy.<locals>.asymptotic_b_large¨  sG  € Ø•UˆFÜ—’˜A“ ! a¥%¬2¯6ª6°!«9Õ!4Õ4ˆBà�Q�q•S•	˜A˜r !�t�HÕ$ q¨$¥w¨r¥zÕ1°A°tµG¸CµKÕ?À!ÀTÅ'È#Å+ÕMØ�T•'˜#•+õØ ! 4¥¨¥õ,Ø./°­hõ7Ø9:¸B¸v½I½õGà˜$•,˜q•.õ!à#)¨4¥<°Õ#3õ4à6<¸dµlÀ2µoõFð ˜$•,˜sÕ"õ#ð &,¨T¥\°#Õ%5õ6ð ð œbŸhšh q¥s›mÕ+¬b¯fªf°Q«iÕ7¸!¼B¿FºFÀ6»NÕ:JÕJˆHØ•7˜XÕ%Ð%r7   c                 ó   <€ S! W4      # rO   r‹   )r˜   r™   r  s   &&€r5   Úasymptotic_a_largeÚ-beta_gen._entropy.<locals>.asymptotic_a_large´  s   ø€ Ù% aÓ+Ð+r7   c                 óê   € \         P                  ! \         P                  ! V 4      4      p\         P                  ! V ^
V,          ,          4      ^,           p\        P                  ! V R8g  W!3R RR7      # )é
   r–   c                 ó0   € V ^
^V,           ,          ,          # )r  r‹   )Úd_Új_s   &&r5   Ú<lambda>Ú<beta_gen._entropy.<locals>.threshold_large.<locals>.<lambda>º  s   € ÀBÈÈaÐRTÍfÍÖDUr7   iè  ©Ú
fill_value)rQ   ÚfloorÚlog10ÚxpxÚapply_where)ÚvÚjÚds   &  r5   Úthreshold_largeÚ*beta_gen._entropy.<locals>.threshold_large·  sT   € Ü—’œŸš !›Ó%ˆAÜ—’˜˜R 1�W�Ó%¨Õ)ˆAÜ—?’? 1¨¡8¨a¨VÑ5UØ.2ô4ð 4r7   g    ÀëRAg    (±RAg    €„.Ar   )
rD   r˜   r™   ró  rþ  r  r  Úthreshold_aÚthreshold_br  s
   &&&      @r5   r  Úbeta_gen._entropy™  s­   ø€ ò	Gò	3ò
	&õ	,ò	4ñ & aÓ(ˆÙ% aÓ(ˆÜ˜Q &™[¨Q°&©[Õ9Ø %™Z¨A­E°S©LÕ9¸QÑ=MÕNØ %™Z¨A­E°S©LÕ9¸QÑ=MÕNØ ™Y¨1¨u©9Õ5ðð
 0Ð1CØ.ð9à˜6ó
ð 	
r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r~   rˆ   r„   r   r×  rK   r	   r   rB   r  r‘   r’   Ú__classcell__©rØ  r”   s   @@r5   rŸ  rŸ  Ä  sr   ù‡ € ñ'òPô
-ò*òò
#ò$ò'ò&ò#õ 4ð" Ù˜}ð 5+ô ,ô
c"ó,ó ðc"÷J.
ò .
r7   rŸ  r©  c                   óp   a € ] tR tRt o Rt]P                  tR tRR lt	R t
R tR tR	 tR
 tR tRtV tR# )Úbetaprime_geniÍ  a'  A beta prime continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `betaprime` is:

.. math::

    f(x, a, b) = \frac{x^{a-1} (1+x)^{-a-b}}{\beta(a, b)}

for :math:`x >= 0`, :math:`a > 0`, :math:`b > 0`, where
:math:`\beta(a, b)` is the beta function (see `scipy.special.beta`).

`betaprime` takes ``a`` and ``b`` as shape parameters.

The distribution is related to the `beta` distribution as follows:
If :math:`X` follows a beta distribution with parameters :math:`a, b`,
then :math:`Y = X/(1-X)` has a beta prime distribution with
parameters :math:`a, b` ([1]_).

The beta prime distribution is a reparametrized version of the
F distribution.  The beta prime distribution with shape parameters
``a`` and ``b`` and ``scale = s`` is equivalent to the F distribution
with parameters ``d1 = 2*a``, ``d2 = 2*b`` and ``scale = (a/b)*s``.
For example,

>>> from scipy.stats import betaprime, f
>>> x = [1, 2, 5, 10]
>>> a = 12
>>> b = 5
>>> betaprime.pdf(x, a, b, scale=2)
array([0.00541179, 0.08331299, 0.14669185, 0.03150079])
>>> f.pdf(x, 2*a, 2*b, scale=(a/b)*2)
array([0.00541179, 0.08331299, 0.14669185, 0.03150079])

%(after_notes)s

References
----------
.. [1] Beta prime distribution, Wikipedia,
       https://en.wikipedia.org/wiki/Beta_prime_distribution

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# r¡  rj   r¢  s   &  r5   rm   Úbetaprime_gen._shape_infoÿ  r¦  r7   Nc                ón   € \         P                  WVR 7      p\         P                  W#VR 7      pWV,          # ©©rô   rõ   )ÚgammaÚrvs)rD   r˜   r™   rô   rõ   Úu1Úu2s   &&&&&  r5   rö   Úbetaprime_gen._rvs  s-   € Ü�Y‰Y�q°,ˆYÓ?ˆÜ�Y‰Y�q°,ˆYÓ?ˆØ�wˆr7   c                óN   € \         P                  ! V P                  WV4      4      # rO   ©rQ   rÓ   rý   r°  s   &&&&r5   ru   Úbetaprime_gen._pdf	  ó   € ä�vŠv�d—l‘l 1¨Ó+Ó,Ð,r7   c                ó¸   € \         P                  ! VR ,
          V4      \         P                  ! W#,           V4      ,
          \         P                  ! W#4      ,
          # r8  )r|   rµ  r´  r¶  r°  s   &&&&r5   rý   Úbetaprime_gen._logpdf  s6   € Ü�xŠx˜˜C� Ó#¤b§j¢j°µ¸Ó&:Õ:¼R¿YºYÀq»_ÕLÐLr7   c                óB   € \         P                  ! V^8„  WV3R R 4      # )rM   c                 óJ   € \         P                  ^^V ,           ,          W!4      # r_   ©r©  r~   ©Úx_Úa_Úb_s   &&&r5   r  Ú$betaprime_gen._cdf.<locals>.<lambda>  s   € œtŸx™x¨¨Q°­V­°bÔ=r7   c                 óJ   € \         P                  V ^V ,           ,          W4      # r_   ©r©  ry   r6  s   &&&r5   r  r:    s   € œtŸy™y¨¨q°2­v­¸Ô?r7   ©r  r  r°  s   &&&&r5   ry   Úbetaprime_gen._cdf  s*   € ô �ŠØ�‰E�A˜!�9Ù=Ù?óAð 	Ar7   c                óB   € \         P                  ! V^8„  WV3R R 4      # )rM   c                 óJ   € \         P                  ^^V ,           ,          W!4      # r_   r<  r6  s   &&&r5   r  Ú#betaprime_gen._sf.<locals>.<lambda>   s   € œtŸy™y¨¨a°"­f­°rÔ>r7   c                 óJ   € \         P                  V ^V ,           ,          W4      # r_   r5  r6  s   &&&r5   r  rA  !  s   € œtŸx™x¨¨a°"­f­°rÔ>r7   r=  r°  s   &&&&r5   r~   Úbetaprime_gen._sf  s(   € Ü�ŠØ�‰E�A˜!�9Ù>Ù>ó@ð 	@r7   c                óJ  € \         P                  ! WV4      w  rp\        P                  P	                  WV4      p\         P
                  ! R R7      ;_uu_ 4        V^V,
          ,          pRRR4       VR8„  p\         P                  ! V4      '       d9   V'       d/   ^\        P                  P                  WV4      ,          ^,
          pX# ^\        P                  P                  W,          W6,          W&,          4      ,          ^,
          XV&   V#   + '       g   i     L¯; i)rl  rm  Ng§èH.ÿï?)rQ   Úbroadcast_arraysÚstatsr©  r„   ro  Úisscalarrˆ   )rD   Úpr˜   r™   ÚrÚoutÚrnear1s   &&&&   r5   r„   Úbetaprime_gen._ppf#  sÇ   € Ü×%Ò% a¨AÓ.‰ˆˆaô �J‰J�O‰O˜A !Ó$ˆÜ�[Š[ ×)Ö)Ø�q˜1•u•+ˆC÷ *à�V‘ˆÜ�;Š;�q�>Š>ßØœŸ
™
Ÿ™¨¨aÓ0Õ0°1Õ4�ð ˆ
ð œEŸJ™JŸO™O¨A­I°qµyÀ!Å)ÓLÕLÈqÕPˆC�‰KØˆ
÷ *×)ús   ÁDÄD"	c                ód   a€ \         P                  ! VS8„  W#3V3R  l\        P                  R7      # )c                 óÆ   <€ \         P                  ! \        ^\        S4      ^,           4       Uu. uF  q V,           ^,
          W,
          ,          NK!  	  up^ R7      # u upi )rM   ©Úaxis)rQ   ÚprodÚranger+  )r˜   r™   Úirc   s   && €r5   r  Ú%betaprime_gen._munp.<locals>.<lambda>8  sB   ø€ œŸš¼¸qÄ#ÀaÃ&ÈÅ(Ô9KÓ!LÑ9K°A Q¥3 q¥5¨1­3§- -Ñ9KÑ!LÐSTÕUùÒ!Ls   °%Ar  ©r  r  rQ   rk   )rD   rc   r˜   r™   s   &f&&r5   r,  Úbetaprime_gen._munp5  s)   ø€ Ü�ŠØ�‰E�A�6ÜUÜ—v‘vôð 	r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   rö   ru   rý   ry   r~   r„   r,  r‘   r’   r“   s   @r5   r"  r"  Í  sH   ø‡ € ñ.ð^ "×4Ñ4€Mòô
ò
-òMòAò@ò÷$ð r7   r"  Ú	betaprimec                   óL   a € ] tR tRt o RtR tR tR tR tRR lt	R t
R	tV tR
# )Úbradford_geni?  a6  A Bradford continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `bradford` is:

.. math::

    f(x, c) = \frac{c}{\log(1+c) (1+cx)}

for :math:`0 <= x <= 1` and :math:`c > 0`.

`bradford` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# ©ÚcFr4  rj   rl   s   &r5   rm   Úbradford_gen._shape_infoU  r6  r7   c                ód   € W"V,          R ,           ,          \         P                  ! V4      ,          # r8  ©r|   ré  ©rD   rt   r\  s   &&&r5   ru   Úbradford_gen._pdfX  s   € à�a•C˜#•I�¤§¢¨!£Õ,Ð,r7   c                óp   € \         P                  ! W!,          4      \         P                  ! V4      ,          # rO   r_  r`  s   &&&r5   ry   Úbradford_gen._cdf\  s   € Ü�xŠx˜�‹}œrŸxšx¨›{Õ*Ð*r7   c                ór   € \         P                  ! V\         P                  ! V4      ,          4      V,          # rO   ©r|   Úexpm1ré  ©rD   rƒ   r\  s   &&&r5   r„   Úbradford_gen._ppf_  s"   € Ü�xŠx˜œBŸHšH Q›K�Ó(¨1Õ,Ð,r7   c                ó¶  € \         P                  ! R V,           4      pW,
          W,          ,          pVR,           V,          RV,          ,
          ^V,          V,          V,          ,          pRpRpRV9   dè   \         P                  ! ^4      ^V,          V,          ^	V,          V,          V^,           ,          ,
          ^V,          V,          W^,           ,          ^,           ,          ,           ,          pV\         P                  ! WV^,
          ,          ^V,          ,           ,          4      ^V,          V^,
          ,          ^V,          ,           ,          ,          pRV9   dò   V^,          V^,
          ,          V^V,          ^,
          ,          ^,           ,          ^V,          V,          V,          V^,
          ,          V^,
          ,          ,           ^V,          V,          V,          ^V,          ^,
          ,          ,           ^V^,          ,          ,           pV^V,          W^,
          ,          ^V,          ,           ^,          ,          ,          pWEWg3# )r–   rÒ   NÚsÚk)rQ   r  r'  )rD   r\  Úmomentsrk  ry  rz  r{  r|  s   &&&     r5   r   Úbradford_gen._statsb  s�  € Ü�FŠF�3�q•5‹MˆØ�c�A•C�[ˆØ�#•�q�y˜˜Q��  1¥ Q¥ q¥Õ)ˆØˆØˆØ�'Œ>Ü—’˜“˜R �T !�V A a¥C¨¥E¨1¨Q­3¥KÕ/°°!µ°Aµ°q¸A½#µw¸qµyÕ0AÕAÕBˆBØ”"—'’'˜!  !¥�W Q q¥S�[�/Ó*¨A¨a­C°°1µ­I°a¸µc­MÕ:Õ:ˆBØ�'Œ>Ø�Q•$˜˜!�•*˜a  1¥ R¥�j¨�mÕ,¨R°­T°!­V°A­X°q¸µs­^¸Q¸q½SÕ-AÕAØ�A•#�a•%˜•'˜1˜Q�3˜r�6Õ"õ#Ø%'¨¨1­¥Wõ-ˆBà�!�A•#�q˜A�#•w˜q �s•{ QÕ&Õ&Õ&ˆBØ˜ˆÐr7   c                ó�   € \         P                  ! ^V,           4      pVR,          \         P                  ! W,          4      ,
          # ©rM   rÒ   rc  )rD   r\  rk  s   && r5   r  Úbradford_gen._entropyq  s,   € Ü�FŠF�1�Q•3‹KˆØ��u”r—v’v˜a�c“{Õ"Ð"r7   r‹   N©Úmvr€  r“   s   @r5   rY  rY  ?  s.   ø‡ € ñò*Eò-ò+ò-ô÷#ð #r7   rY  Úbradfordc                   óf   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tR tRtV tR# )Úburr_geniy  a  A Burr (Type III) continuous random variable.

%(before_notes)s

See Also
--------
fisk : a special case of either `burr` or `burr12` with ``d=1``
burr12 : Burr Type XII distribution
mielke : Mielke Beta-Kappa / Dagum distribution

Notes
-----
The probability density function for `burr` is:

.. math::

    f(x; c, d) = c d \frac{x^{-c - 1}}
                          {{(1 + x^{-c})}^{d + 1}}

for :math:`x >= 0` and :math:`c, d > 0`.

`burr` takes ``c`` and ``d`` as shape parameters for :math:`c` and
:math:`d`.

This is the PDF corresponding to the third CDF given in Burr's list;
specifically, it is equation (11) in Burr's paper [1]_. The distribution
is also commonly referred to as the Dagum distribution [2]_. If the
parameter :math:`c < 1` then the mean of the distribution does not
exist and if :math:`c < 2` the variance does not exist [2]_.
The PDF is finite at the left endpoint :math:`x = 0` if :math:`c * d >= 1`.

%(after_notes)s

References
----------
.. [1] Burr, I. W. "Cumulative frequency functions", Annals of
   Mathematical Statistics, 13(2), pp 215-232 (1942).
.. [2] https://en.wikipedia.org/wiki/Dagum_distribution
.. [3] Kleiber, Christian. "A guide to the Dagum distributions."
   Modeling Income Distributions and Lorenz Curves  pp 97-117 (2008).

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# ©r\  Fr  r4  rj   ©rD   ÚicÚids   &  r5   rm   Úburr_gen._shape_infoª  r¦  r7   c                óz   € \         P                  ! V^ 8H  WV3R R 4      pVP                  ^ 8X  d
   VR,          # T# )r   c                 óp   € W,          WV,          ^,
          ,          ,          ^W,          ,           ,          # r_   r‹   ©r7  Úc_r  s   &&&r5   r  Úburr_gen._pdf.<locals>.<lambda>³  s    € ˜r�w¨"°"­u°Q­w­-Õ8¸AÀÅ½JÖGr7   c                 ó‚   € W,          W) R ,
          ,          ,          ^W) ,          ,           VR ,           ,          ,          # r8  r‹   r~  s   &&&r5   r  r€  ´  s.   €  ¥¨2°#¸µ)Õ+<Õ =Ø"# b¨S¥k¥/°r¸CµxÕ!@ö!Br7   r‹   ©r  r  Úndim©rD   rt   r\  r  Úoutputs   &&&& r5   ru   Úburr_gen._pdf¯  sC   € ä—’Ø�‰F�Q˜1�IÙGñCóDˆð
 $Ÿ[™[¨AÔ-ˆv�b�zÐ9°6Ð9r7   c                óz   € \         P                  ! V^ 8H  WV3R R 4      pVP                  ^ 8X  d
   VR,          # T# )r   c                 ó  € \         P                  ! V4      \         P                  ! V4      ,           \        P                  ! W,          ^,
          V 4      ,           V^,           \        P                  ! W,          4      ,          ,
          # r_   )rQ   r  r|   rµ  ré  r~  s   &&&r5   r  Ú"burr_gen._logpdf.<locals>.<lambda>»  sK   € ¤§¢ r£
¬R¯VªV°B«ZÕ 7¼"¿(º(À2Å5È1Å9ÈbÓ:QÕ QØ#% a¥4¬2¯8ª8°BµHÓ+=Õ"=ö!>r7   c                 ó   € \         P                  ! V4      \         P                  ! V4      ,           \        P                  ! V) ^,
          V 4      ,           \        P                  ! V^,           W) ,          4      ,
          # r_   ©rQ   r  r|   rµ  r´  r~  s   &&&r5   r  r‰  ½  sM   € ¤§¢ r£
¬R¯VªV°B«ZÕ 7Ü"$§(¢(¨B¨3°­7°BÓ"7õ!8ä"$§*¢*¨R°­T°2¸µ9Ó"=ö!>r7   r‹   r‚  r„  s   &&&& r5   rý   Úburr_gen._logpdf¸  sD   € Ü—’Ø�‰F�Q˜1�Iñ?ñ?ó	@ˆð $Ÿ[™[¨AÔ-ˆv�b�zÐ9°6Ð9r7   c                ó2   € ^W) ,          ,           V) ,          # r_   r‹   ©rD   rt   r\  r  s   &&&&r5   ry   Úburr_gen._cdfÂ  s   € Ø�A˜•G• ˜rÕ"Ð"r7   c                óL   € \         P                  ! W) ,          4      V) ,          # rO   r_  rŽ  s   &&&&r5   r  Úburr_gen._logcdfÅ  s   € Ü�xŠx˜˜B�Ó  Q BÕ'Ð'r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   ©rQ   rÓ   r
  rŽ  s   &&&&r5   r~   Úburr_gen._sfÈ  ó   € Ü�vŠv�d—k‘k !¨Ó*Ó+Ð+r7   c                ó\   € \         P                  ! ^W) ,          ,           V) ,          ) 4      # r_   ©rQ   ré  rŽ  s   &&&&r5   r
  Úburr_gen._logsfË  s#   € Ü�xŠx˜1˜q 2�w�;¨1¨"Õ-Ð-Ó.Ð.r7   c                óL   € VRV,          ,          ^,
          RV,          ,          # ©r–   ç      ð¿r‹   ©rD   rƒ   r\  r  s   &&&&r5   r„   Úburr_gen._ppfÎ  s   € Ø�D˜•F•˜a• 4¨¥6Õ*Ð*r7   c                óˆ   € \         P                  ! RV,          V) 4      p\         P                  ! V4      RV,          ,          # rš  ©r|   r´  rf  )rD   rƒ   r\  r  Ú_qs   &&&& r5   rˆ   Úburr_gen._isfÑ  s/   € Ü�ZŠZ˜˜q� 1 "Ó%ˆÜ�xŠx˜‹|  q¥Õ)Ð)r7   c                óð  € \         P                  ! ^^4      P                  ^^4      V,          p\        P                  ! W#,           RV,
          4      V,          w  rErg\         P
                  ! VR8„  V\         P                  4      pWX^,          ,
          p	\         P
                  ! VR8„  V	\         P                  4      p
\        P                  ! VR8„  WEWi3R \         P                  R7      p\        P                  ! VR8„  WEWgV	3R \         P                  R7      p\         P                  ! V4      ^ 8X  d?   VP                  4       V
P                  4       VP                  4       VP                  4       3# WŠW¼3# )rM   r–   rÒ   ç      @c                 óž   € V^V,          V ,          ,
          ^V ^,          ,          ,           \         P                  ! V^,          4      ,          # ©é   rÇ  )Úe1Úe2Úe3Úmu2_if_cs   &&&&r5   r  Ú!burr_gen._stats.<locals>.<lambda>Þ  s3   € ¨2°°"µ°Rµ­<¸!¸BÀ½E½'Õ+AÜ-/¯WªW°hÀµ]Ó-Cö+Dr7   r  ç      @c                 ó¼   € V^V,          V ,          ,
          ^V,          V ^,          ,          ,           ^V ^,          ,          ,
          V^,          ,          ^,
          # r\  r‹   )r§  r¨  r©  Úe4rª  s   &&&&&r5   r  r«  ã  s=   € Ø�q˜•t˜B•w•,  2¥ b¨!¥e¥Õ+¨a°°Aµ­gÕ5¸À1½ÕDÈÖIr7   )rQ   ÚarangeÚreshaper|   r©  ÚwhererF  r  r  rƒ  Úitem)rD   r\  r  Úncr§  r¨  r©  r®  ry  rª  rz  r{  r|  s   &&&          r5   r   Úburr_gen._statsÕ  s  € Ü�YŠY�q˜!‹_×$Ñ$ Q qÓ)¨AÕ-ˆäŸš ¥¨¨b­Ó1°AÕ5‰ˆ�Ü�XŠX�a˜#‘g˜r¤2§6¡6Ó*ˆØ˜A�•:ˆÜ�hŠh�q˜3‘w ¬"¯&©&Ó1ˆÜ�_Š_Ø�‰G�b˜bÐ+ñEä—v‘vô	ˆô
 �_Š_Ø�‰G�b˜b hÐ/ñKä—v‘vô	ˆô
 �7Š7�1‹:˜Œ?Ø—7‘7“9˜cŸh™h›j¨"¯'©'«)°R·W±W³YÐ>Ð>Ø˜ˆÐr7   c                ó  € R  p\         P                  ! V4      \         P                  ! V4      \         P                  ! V4      r2p\        P                  ! W!8„  W8H  ,          W38H  ,          WV3V\         P                  R7      # )c                 óx   € R V ,          V,          pV\         P                  ! R V,
          W#,           4      ,          # r8  ©r|   r©  ©rc   r\  r  r³  s   &&& r5   Ú__munpÚburr_gen._munp.<locals>.__munpë  ó+   € Ø�a•˜!•ˆBØ”r—w’w˜s R�x¨­Ó0Õ0Ð0r7   r  )rQ   r#  r  r  rF  )rD   rc   r\  r  Ú_burr_gen__munps   &&&& r5   r,  Úburr_gen._munpê  s`   € ò	1ô —*’*˜Q“-¤§¢¨A£´·
²
¸1³ˆaˆÜ�Š ¡¨!©&Õ1°Q±VÕ<Ø ! a˜y¨&¼R¿V¹VôEð 	Er7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r  r~   r
  r„   rˆ   r   r,  r‘   r’   r“   s   @r5   ru  ru  y  sI   ø‡ € ñ+ò`ò
:ò:ò#ò(ò,ò/ò+ò*ò÷*Eð Er7   ru  Úburrc                   ó`   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tRtV tR# )Ú
burr12_geniö  a  A Burr (Type XII) continuous random variable.

%(before_notes)s

See Also
--------
fisk : a special case of either `burr` or `burr12` with ``d=1``
burr : Burr Type III distribution

Notes
-----
The probability density function for `burr12` is:

.. math::

    f(x; c, d) = c d \frac{x^{c-1}}
                          {(1 + x^c)^{d + 1}}

for :math:`x >= 0` and :math:`c, d > 0`.

`burr12` takes ``c`` and ``d`` as shape parameters for :math:`c`
and :math:`d`.

This is the PDF corresponding to the twelfth CDF given in Burr's list;
specifically, it is equation (20) in Burr's paper [1]_.

%(after_notes)s

The Burr type 12 distribution is also sometimes referred to as
the Singh-Maddala distribution from NIST [2]_.

References
----------
.. [1] Burr, I. W. "Cumulative frequency functions", Annals of
   Mathematical Statistics, 13(2), pp 215-232 (1942).

.. [2] https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/b12pdf.htm

.. [3] "Burr distribution",
   https://en.wikipedia.org/wiki/Burr_distribution

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# rw  rj   rx  s   &  r5   rm   Úburr12_gen._shape_info#  r¦  r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  rŽ  s   &&&&r5   ru   Úburr12_gen._pdf(  r0  r7   c                óþ   € \         P                  ! V4      \         P                  ! V4      ,           \        P                  ! V^,
          V4      ,           \        P                  ! V) ^,
          W,          4      ,           # r_   r‹  rŽ  s   &&&&r5   rý   Úburr12_gen._logpdf,  sI   € Ü�vŠv�a‹yœ2Ÿ6š6 !›9Õ$¤r§x¢x°°Aµ°qÓ'9Õ9¼B¿JºJÈÀrÈ!ÅtÈQÍTÓ<RÕRÐRr7   c                óP   € \         P                  ! V P                  WV4      4      ) # rO   ©r|   rf  r
  rŽ  s   &&&&r5   ry   Úburr12_gen._cdf/  ó   € Ü—’˜Ÿ™ Q¨1Ó-Ó.Ð.Ð.r7   c                óZ   € \         P                  ! ^W,          ,           V) ,          ) 4      # r_   r_  rŽ  s   &&&&r5   r  Úburr12_gen._logcdf2  s!   € Ü�xŠx˜!˜a�d�( q bÕ)Ð)Ó*Ð*r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r“  rŽ  s   &&&&r5   r~   Úburr12_gen._sf5  r•  r7   c                ó>   € \         P                  ! V) W,          4      # rO   ©r|   r´  rŽ  s   &&&&r5   r
  Úburr12_gen._logsf8  s   € Ü�zŠz˜1˜"˜a�dÓ#Ð#r7   c                ó�   € \         P                  ! RV,          \         P                  ! V) 4      ,          4      ^V,          ,          # ©rM   r  re  rœ  s   &&&&r5   r„   Úburr12_gen._ppf;  s/   € ô �xŠx˜˜1�œrŸxšx¨¨›|Õ+Ó,¨q°­sÕ3Ð3r7   c                óŽ   € \         P                  ! RV,          \        P                  ! V4      ,          4      ^V,          ,          # rÓ  )r|   rf  rQ   r  )rD   rH  r\  r  s   &&&&r5   rˆ   Úburr12_gen._isfA  s+   € Ü�xŠx˜˜1�œrŸvšv a›yÕ(Ó)¨A¨a­CÕ0Ð0r7   c                ón   € R  p\         P                  ! W#,          V8„  WV3V\        P                  R7      # )c                 óx   € R V ,          V,          pV\         P                  ! R V,           W#,
          4      ,          # r8  r·  r¸  s   &&& r5   Úmoment_if_existsÚ*burr12_gen._munp.<locals>.moment_if_existsE  r»  r7   r  ©r  r  rQ   rF  )rD   rc   r\  r  rÙ  s   &&&& r5   r,  Úburr12_gen._munpD  s2   € ò	1ô �Š˜q�u q™y¨1°¨)Ð5EÜ*,¯&©&ô2ð 	2r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r  r~   r
  r„   rˆ   r,  r‘   r’   r“   s   @r5   rÀ  rÀ  ö  sC   ø‡ € ñ+òXò
-òSò/ò+ò,ò$ò4ò1÷2ð 2r7   rÀ  Úburr12c                   ól   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tRtV tR# )Úfisk_geniP  aV  A Fisk continuous random variable.

The Fisk distribution is also known as the log-logistic distribution.

%(before_notes)s

See Also
--------
burr

Notes
-----
The probability density function for `fisk` is:

.. math::

    f(x, c) = \frac{c x^{c-1}}
                   {(1 + x^c)^2}

for :math:`x >= 0` and :math:`c > 0`.

Please note that the above expression can be transformed into the following
one, which is also commonly used:

.. math::

    f(x, c) = \frac{c x^{-c-1}}
                   {(1 + x^{-c})^2}

`fisk` takes ``c`` as a shape parameter for :math:`c`.

`fisk` is a special case of `burr` or `burr12` with ``d=1``.

Suppose ``X`` is a logistic random variable with location ``l``
and scale ``s``. Then ``Y = exp(X)`` is a Fisk (log-logistic)
random variable with ``scale = exp(l)`` and shape ``c = 1/s``.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úfisk_gen._shape_info{  r6  r7   c                ó.   € \         P                  WR 4      # r8  )r¾  ru   r`  s   &&&r5   ru   Úfisk_gen._pdf~  s   € ä�y‰y˜˜sÓ#Ð#r7   c                ó.   € \         P                  WR 4      # r8  )r¾  ry   r`  s   &&&r5   ry   Úfisk_gen._cdf‚  ó   € Ü�y‰y˜˜sÓ#Ð#r7   c                ó.   € \         P                  WR 4      # r8  )r¾  r~   r`  s   &&&r5   r~   Úfisk_gen._sf…  s   € Ü�x‰x˜˜cÓ"Ð"r7   c                ó.   € \         P                  WR 4      # r8  )r¾  rý   r`  s   &&&r5   rý   Úfisk_gen._logpdfˆ  s   € ä�|‰|˜A #Ó&Ð&r7   c                ó.   € \         P                  WR 4      # r8  )r¾  r  r`  s   &&&r5   r  Úfisk_gen._logcdfŒ  s   € Ü�|‰|˜A #Ó&Ð&r7   c                ó.   € \         P                  WR 4      # r8  )r¾  r
  r`  s   &&&r5   r
  Úfisk_gen._logsf�  s   € Ü�{‰{˜1 Ó%Ð%r7   c                ó.   € \         P                  WR 4      # r8  )r¾  r„   r`  s   &&&r5   r„   Úfisk_gen._ppf’  ræ  r7   c                ó.   € \         P                  WR 4      # r8  )r¾  rˆ   rg  s   &&&r5   rˆ   Úfisk_gen._isf•  ræ  r7   c                ó.   € \         P                  WR 4      # r8  )r¾  r,  ©rD   rc   r\  s   &&&r5   r,  Úfisk_gen._munp˜  s   € Ü�z‰z˜! Ó$Ð$r7   c                ó.   € \         P                  VR 4      # r8  )r¾  r   ©rD   r\  s   &&r5   r   Úfisk_gen._stats›  s   € Ü�{‰{˜1˜cÓ"Ð"r7   c                ó<   € ^\         P                  ! V4      ,
          # rD  rc  r÷  s   &&r5   r  Úfisk_gen._entropyž  ó   € Ø”2—6’6˜!“9�}Ðr7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   ry   r~   rý   r  r
  r„   rˆ   r,  r   r  r‘   r’   r“   s   @r5   rß  rß  P  sM   ø‡ € ñ)òTEò$ò$ò#ò'ò'ò&ò$ò$ò%ò#÷ð r7   rß  Úfiskc                   ód   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tRR ltRtV tR# )Ú
cauchy_geni¥  aÂ  A Cauchy continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `cauchy` is

.. math::

    f(x) = \frac{1}{\pi (1 + x^2)}

for a real number :math:`x`.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``ppf`` and ``isf`` methods. [1]_

%(after_notes)s

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úcauchy_gen._shape_infoÀ  r¼   r7   c                óÔ   € \         P                  ! R R7      ;_uu_ 4        R\         P                  ,          RW,          ,           ,          uuRRR4       #   + '       g   i     R# ; i)rl  r­  r–   N)rQ   ro  r  r¿   s   &&r5   ru   Úcauchy_gen._pdfÃ  s6   € ä�[Š[˜h×'Ö'Ø”r—u‘u•9˜c !¥#�gÕ&÷ (×'×'Ó'ús    +AÁA'	c                ój   € \         P                  ! V4      p\        P                  ! V^8  VR R 4      # )rM   c                 óT   € \         ) \        P                  ! V ^,          4      ,
          # rD  )r'   rQ   ré  ©Úabsxs   &r5   r  Ú$cauchy_gen._logpdf.<locals>.<lambda>Ô  s   € œ'˜¤B§H¢H¨T°1­WÓ$5Ö5r7   c                 ó¦   € \         ) ^\        P                  ! V 4      ,          \        P                  ! ^V ,          ^,          4      ,           ,
          # rD  )r'   rQ   r  ré  r  s   &r5   r  r  Õ  s-   € œ7˜( a¬¯ª¨t«¥n´r·x²xÀÀ4ÅÈ!ÅÓ7LÕ&LÖMr7   )rQ   Úabsr  r  )rD   rt   r  s   && r5   rý   Úcauchy_gen._logpdfÈ  s5   € ô �vŠv�a‹yˆô �ŠØ�1‰H�dÙ5ÙNóPð 	Pr7   c                ó\   € \         P                  ! ^V) 4      \         P                  ,          # r_   ©rQ   Úarctan2r  r¿   s   &&r5   ry   Úcauchy_gen._cdf×  s   € Ü�zŠz˜!˜a˜RÓ ¤§¡Õ&Ð&r7   c                ó2   € \         P                  ! V^ ^4      # ©r   )rq   Ú_cauchy_ppfrÉ   s   &&r5   r„   Úcauchy_gen._ppfÚ  ó   € Ü�Š˜q ! QÓ'Ð'r7   c                óZ   € \         P                  ! ^V4      \         P                  ,          # r_   r  r¿   s   &&r5   r~   Úcauchy_gen._sfÝ  s   € Ü�zŠz˜!˜QÓ¤§¡Õ%Ð%r7   c                ó2   € \         P                  ! V^ ^4      # r  )rq   Ú_cauchy_isfrÉ   s   &&r5   rˆ   Úcauchy_gen._isfà  r  r7   c                ó~   € \         P                  \         P                  \         P                  \         P                  3# rO   ©rQ   rF  rl   s   &r5   r   Úcauchy_gen._statsã  ó!   € Ü�v‰v”r—v‘vœrŸv™v¤r§v¡vÐ-Ð-r7   c                óX   € \         P                  ! ^\         P                  ,          4      # r\  r  rl   s   &r5   r  Úcauchy_gen._entropyæ  ó   € Ü�vŠv�aœŸ™•g‹Ðr7   Nc                ó¨   € \        V\        4      '       d   VP                  4       p\        P                  ! V. RO4      w  r4pWEV,
          ^,          3# ©é   ©r"  é2   éK   ©r>   r)   rÕ  rQ   Ú
percentile©rD   rE   rF   Úp25Úp50Úp75s   &&&   r5   r×  Úcauchy_gen._fitstarté  ó@   € ä�dœL×)Ò)Ø—>‘>Ó#ˆDÜŸš dªLÓ9‰ˆ�#Ø˜3•Y •MÐ!Ð!r7   r‹   rO   )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   rˆ   r   r  r×  r‘   r’   r“   s   @r5   rþ  rþ  ¥  sB   ø‡ € ñò4ò'ò
Pò'ò(ò&ò(ò.ò÷"ò "r7   rþ  Úcauchyc                   ód   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tRtV tR# )Úchi_geniô  a—  A chi continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `chi` is:

.. math::

    f(x, k) = \frac{1}{2^{k/2-1} \Gamma \left( k/2 \right)}
               x^{k-1} \exp \left( -x^2/2 \right)

for :math:`x >= 0` and :math:`k > 0` (degrees of freedom, denoted ``df``
in the implementation). :math:`\Gamma` is the gamma function
(`scipy.special.gamma`).

Special cases of `chi` are:

    - ``chi(1, loc, scale)`` is equivalent to `halfnorm`
    - ``chi(2, 0, scale)`` is equivalent to `rayleigh`
    - ``chi(3, 0, scale)`` is equivalent to `maxwell`

`chi` takes ``df`` as a shape parameter.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# ©ÚdfFr4  rj   rl   s   &r5   rm   Úchi_gen._shape_info  ó   € Ü˜4 ¨¬B¯F©F¨°^ÓDÐEÐEr7   Nc                óX   € \         P                  ! \        P                  WVR 7      4      # r&  )rQ   r'  Úchi2r)  ©rD   r3  rô   rõ   s   &&&&r5   rö   Úchi_gen._rvs  s   € Ü�wŠw”t—x‘x ¸L�xÓIÓJÐJr7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  ©rD   rt   r3  s   &&&r5   ru   Úchi_gen._pdf  s   € ô �vŠv�d—l‘l 1Ó)Ó*Ð*r7   c                ó8  € \         P                  ! ^4      R\         P                  ! ^4      ,          V,          ,
          \        P                  ! RV,          4      ,
          pV\        P                  ! VR,
          V4      ,           RV^,          ,          ,
          # )rÑ   r£   r–   )rQ   r  r|   r  rµ  )rD   rt   r3  Úls   &&& r5   rý   Úchi_gen._logpdf  s]   € Ü�FŠF�1‹I˜œ2Ÿ6š6 !›9� R�Õ'¬"¯*ª*°R¸µUÓ*;Õ;ˆØ”2—8’8˜B �G QÓ'Õ'¨"¨Q°­T­'Õ1Ð1r7   c                óZ   € \         P                  ! R V,          R V^,          ,          4      # r  ©r|   Úgammaincr;  s   &&&r5   ry   Úchi_gen._cdf#  s   € Ü�{Š{˜2˜b�5 " Q¨¥T¥'Ó*Ð*r7   c                óZ   € \         P                  ! R V,          R V^,          ,          4      # r  ©r|   Ú	gammainccr;  s   &&&r5   r~   Úchi_gen._sf&  s   € Ü�|Š|˜B˜r�E 2 a¨¥d¥7Ó+Ð+r7   c                ót   € \         P                  ! ^\        P                  ! RV,          V4      ,          4      # ©rÑ   r£   ©rQ   r'  r|   Úgammaincinv©rD   rƒ   r3  s   &&&r5   r„   Úchi_gen._ppf)  s%   € Ü�wŠw�qœŸš¨¨2­¨qÓ1Õ1Ó2Ð2r7   c                ót   € \         P                  ! ^\        P                  ! RV,          V4      ,          4      # rI  ©rQ   r'  r|   ÚgammainccinvrL  s   &&&r5   rˆ   Úchi_gen._isf,  s%   € Ü�wŠw�qœŸš¨¨B­°Ó2Õ2Ó3Ð3r7   c                óF  € \         P                  ! ^4      \        P                  ! RV,          R4      ,          pWV,          ,
          p^VR,          ,          V^^V,          ,
          ,          ,           \         P                  ! \         P
                  ! VR4      4      ,          p^V,          RV,
          ,          ^V^,          ,          ,
          ^V^,          ,          ^V,          ^,
          ,          ,           pV\         P                  ! VR,          4      ,          pW#WE3# )rÑ   r£   r£  ç      ø?r–   rÒ   )rQ   r'  r|   Úpochr#  Úpower©rD   r3  ry  rz  r{  r|  s   &&    r5   r   Úchi_gen._stats/  s¾   € ä�WŠW�Q‹Zœ"Ÿ'š' #¨¥(¨CÓ0Õ0ˆØ�b•5�jˆØ��C•�i˜"˜a  "¥�f�+Õ%¤r§z¢z´"·(²(¸3ÀÓ2DÓ'EÕEˆØˆr�T�3�r•6�]˜1˜R �U�7Õ" Q r¨1¥u¥W°°"µ°QµÕ%7Õ7ˆØ
Œb�jŠj˜˜c�Ó"Õ"ˆØ˜ˆÐr7   c                óD   € R  pR p\         P                  ! VR8  WV4      # )c                 óî   € \         P                  ! R V ,          4      R V \        P                  ! ^4      ,
          V ^,
          \         P                  ! R V ,          4      ,          ,
          ,          ,           # r  )r|   r  rQ   r  Údigamma©r3  s   &r5   Úregular_formulaÚ)chi_gen._entropy.<locals>.regular_formula:  sM   € Ü—J’J˜r B�wÓ'Ø˜R¤"§&¢&¨£)�^¨r°A­v¼¿ºÀCÈ"ÅHÓ9MÕ.MÕMÕNõOð Pr7   c                 ó  € R \         P                  ! \         P                  4      ^,          ,           V R,          ^,          ,
          V R,          ^,          ,
          RV R,          ,          ,
          V R,          ^,          ,           # )r£   r  r<  glÁlÁ¶?éýÿÿÿéüÿÿÿr  r[  s   &r5   Úasymptotic_formulaÚ,chi_gen._entropy.<locals>.asymptotic_formula>  sY   € Øœ"Ÿ&š&¤§¡›-¨�/Õ)¨R°­V°Q­JÕ6¸"¸b½&À!½ÕCØ˜B �F•mõ$Ø')¨2¥v¨r¥kõ2ð 3r7   i,  r=  )rD   r3  r\  ra  s   &&  r5   r  Úchi_gen._entropy8  s'   € ò	Pò	3ô �Š˜r C™x¨Ð>PÓQÐQr7   r‹   r.  ©rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r~   r„   rˆ   r   r  r‘   r’   r“   s   @r5   r0  r0  ô  sE   ø‡ € ñò<FôKò+ò2ò+ò,ò3ò4ò÷
Rð 
Rr7   r0  Úchic                   ód   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tRtV tR# )Úchi2_geniH  a|  A chi-squared continuous random variable.

For the noncentral chi-square distribution, see `ncx2`.

%(before_notes)s

See Also
--------
ncx2

Notes
-----
The probability density function for `chi2` is:

.. math::

    f(x, k) = \frac{1}{2^{k/2} \Gamma \left( k/2 \right)}
               x^{k/2-1} \exp \left( -x/2 \right)

for :math:`x > 0`  and :math:`k > 0` (degrees of freedom, denoted ``df``
in the implementation).

`chi2` takes ``df`` as a shape parameter.

The chi-squared distribution is a special case of the gamma
distribution, with gamma parameters ``a = df/2``, ``loc = 0`` and
``scale = 2``.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r2  rj   rl   s   &r5   rm   Úchi2_gen._shape_infoj  r5  r7   Nc                ó$   € VP                  W4      # rO   )Ú	chisquarer8  s   &&&&r5   rö   Úchi2_gen._rvsm  s   € Ø×%Ñ% bÓ/Ð/r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r;  s   &&&r5   ru   Úchi2_gen._pdfp  s   € ä�vŠv�d—l‘l 1Ó)Ó*Ð*r7   c                óþ   € \         P                  ! VR ,          ^,
          V4      VR ,          ,
          \         P                  ! VR ,          4      ,
          \        P                  ! ^4      V,          R ,          ,
          # rr  )r|   rµ  r  rQ   r  r;  s   &&&r5   rý   Úchi2_gen._logpdft  sM   € Ü�xŠx˜˜2�˜a� Ó# a¨¥dÕ*¬R¯ZªZ¸¸2½Ó->Õ>Ä"Ç&Â&ÈÃ)ÈBÅ,ÐPRÕARÕRÐRr7   c                ó.   € \         P                  ! W!4      # rO   )r|   Úchdtrr;  s   &&&r5   ry   Úchi2_gen._cdfw  ó   € Ü�xŠx˜‹Ðr7   c                ó.   € \         P                  ! W!4      # rO   )r|   Úchdtrcr;  s   &&&r5   r~   Úchi2_gen._sfz  ó   € Ü�yŠy˜ÓÐr7   c                ó.   € \         P                  ! W!4      # rO   )r|   Úchdtri©rD   rH  r3  s   &&&r5   rˆ   Úchi2_gen._isf}  rx  r7   c                óL   € ^\         P                  ! V^,          V4      ,          # rD  ©r|   rK  r{  s   &&&r5   r„   Úchi2_gen._ppf€  s   € Ø”—’  1¥ aÓ(Õ(Ð(r7   c                óz   € Tp^V,          p^\         P                  ! RV,          4      ,          pRV,          pW#WE3# )rÑ   rÒ   ç      (@rÇ  rV  s   &&    r5   r   Úchi2_gen._statsƒ  s9   € ØˆØ��dˆØŒr�wŠw�s˜2•v‹ÕˆØ�"�WˆØ˜ˆÐr7   c                óV   € R V,          pR pR p\         P                  ! V^}8  VW44      # )r£   c                 óÄ   € V \         P                  ! ^4      ,           \        P                  ! V 4      ,           ^V ,
          \        P                  ! V 4      ,          ,           # rD  )rQ   r  r|   r  r•  )Úhalf_dfs   &r5   r\  Ú*chi2_gen._entropy.<locals>.regular_formula�  s>   € ØœbŸfšf Q›iÕ'¬"¯*ª*°WÓ*=Õ=Ø˜•[¤B§F¢F¨7£OÕ3õ4ð 5r7   c                 ót  € \         P                  ! ^4      R^\         P                  ! ^\         P                  ,          4      ,           ,          ,           pRV ,          pVRVRVRVR,          ,           ,          ,           ,          ,           ,          R\         P                  ! V 4      ,          ,           V,           # )rÑ   r£   g      @gUUUUUUå¿çUUUUUUÕ¿glÁlÁ¶¿r  )r…  r\  Úhs   &  r5   ra  Ú-chi2_gen._entropy.<locals>.asymptotic_formula‘  s   € ô —’�q“	˜C ¤R§V¢V¨A¬b¯e©e­G£_Õ!4Õ5Õ5ˆAØ�G•ˆAØ�t˜a ¨¨5°1°Sµ5­=Õ(9Õ!9Õ:Õ:Õ;ØœŸš˜w›Õ'õ(Ø*+õ,ð -r7   r=  )rD   r3  r…  r\  ra  s   &&   r5   r  Úchi2_gen._entropyŠ  s5   € Ø˜•(ˆò	5ò		-ô �Š˜w¨™}¨gØ.óDð 	Dr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r~   rˆ   r„   r   r  r‘   r’   r“   s   @r5   rg  rg  H  sF   ø‡ € ñ òBFô0ò+òSòò ò ò)ò÷Dð Dr7   rg  r7  c                   óZ   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tRtV tR# )Ú
cosine_geni£  a0  A cosine continuous random variable.

%(before_notes)s

Notes
-----
The cosine distribution is an approximation to the normal distribution.
The probability density function for `cosine` is:

.. math::

    f(x) = \frac{1}{2\pi} (1+\cos(x))

for :math:`-\pi \le x \le \pi`.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úcosine_gen._shape_info¸  r¼   r7   c                ót   € R\         P                  ,          ^\         P                  ! V4      ,           ,          # ©r–   r£   ©rQ   r  rQ  r¿   s   &&r5   ru   Úcosine_gen._pdf»  s!   € à”R—U‘U�{˜AœbŸfšf Q›i�KÕ(Ð(r7   c                óˆ   € \         P                  ! V4      p\        P                  ! VR8g  VR \         P                  ) R7      # )rM   c                 óŽ   € \         P                  ! V 4      \         P                  ! ^\         P                  ,          4      ,
          # rD  )rQ   ré  r  r  ©r\  s   &r5   r  Ú$cosine_gen._logpdf.<locals>.<lambda>Â  s!   € ¬¯ª°!«´r·v²v¸aÄÇÁ½g³Ö)Fr7   r  r  )rQ   rQ  r  r  rk   r`  s   && r5   rý   Úcosine_gen._logpdf¿  s4   € Ü�FŠF�1‹IˆÜ�Š˜q B™w¨ÙFÜ+-¯6©6¨'ô3ð 	3r7   c                ó.   € \         P                  ! V4      # rO   ©rq   Ú_cosine_cdfr¿   s   &&r5   ry   Úcosine_gen._cdfÅ  s   € Ü�Š˜qÓ!Ð!r7   c                ó0   € \         P                  ! V) 4      # rO   rš  r¿   s   &&r5   r~   Úcosine_gen._sfÈ  s   € Ü�Š ˜rÓ"Ð"r7   c                ó.   € \         P                  ! V4      # rO   ©rq   Ú_cosine_invcdf©rD   rH  s   &&r5   r„   Úcosine_gen._ppfË  s   € Ü×!Ò! !Ó$Ð$r7   c                ó0   € \         P                  ! V4      ) # rO   r   r¢  s   &&r5   rˆ   Úcosine_gen._isfÎ  s   € Ü×"Ò" 1Ó%Ð%Ð%r7   c                ó<  € \         P                  \         P                  ,          R ,          R,
          pR\         P                  ^,          ^Z,
          ,          R\         P                  \         P                  ,          ^,
          ^,          ,          ,          pRVRV3# )r£  rÒ   ç      @r•   r  r`  )rD   r  rk  s   &  r5   r   Úcosine_gen._statsÑ  sa   € Ü�U‰U”R—U‘U�]˜SÕ  CÕ'ˆØ”B—E‘E˜1•H˜r•MÕ" c¬R¯U©U´R·U±U­]¸QÕ->ÀÕ,BÕ&BÕCˆØ�A�s˜Aˆ~Ðr7   c                óf   € \         P                  ! ^\         P                  ,          4      R,
          # )rU  r–   r  rl   s   &r5   r  Úcosine_gen._entropyÖ  s   € Ü�vŠv�aœŸ™•g‹˜sÕ"Ð"r7   r‹   N©rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r~   r„   rˆ   r   r  r‘   r’   r“   s   @r5   r�  r�  £  s<   ø‡ € ñò(ò)ò3ò"ò#ò%ò&ò÷
#ð #r7   r�  Úcosinec                   ód   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tRtV tR# )Ú
dgamma_geniÝ  aˆ  A double gamma continuous random variable.

The double gamma distribution is also known as the reflected gamma
distribution [1]_.

%(before_notes)s

Notes
-----
The probability density function for `dgamma` is:

.. math::

    f(x, a) = \frac{1}{2\Gamma(a)} |x|^{a-1} \exp(-|x|)

for a real number :math:`x` and :math:`a > 0`. :math:`\Gamma` is the
gamma function (`scipy.special.gamma`).

`dgamma` takes ``a`` as a shape parameter for :math:`a`.

%(after_notes)s

References
----------
.. [1] Johnson, Kotz, and Balakrishnan, "Continuous Univariate
       Distributions, Volume 1", Second Edition, John Wiley and Sons
       (1994).

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r3  rj   rl   s   &r5   rm   Údgamma_gen._shape_infoý  r6  r7   Nc                ó˜   € VP                  VR 7      p\        P                  WVR7      pV\        P                  ! VR8¬  ^R4      ,          # ©©rô   r'  r£   r  )Úuniformr(  r)  rQ   r±  )rD   r˜   rô   rõ   ÚuÚgms   &&&&  r5   rö   Údgamma_gen._rvs   sC   € Ø× Ñ  dÐ Ó+ˆÜ�Y‰Y�q°,ˆYÓ?ˆØ”B—H’H˜Q #™X q¨"Ó-Õ-Ð-r7   c                óÀ   € \        V4      pR ^\        P                  ! V4      ,          ,          W2R ,
          ,          ,          \        P                  ! V) 4      ,          # r8  )r	  r|   r(  rQ   rÓ   ©rD   rt   r˜   Úaxs   &&& r5   ru   Údgamma_gen._pdf  s<   € ä�‹VˆØ�A”b—h’h˜q“k•MÕ" 2¨#­¥;Õ.´·²¸¸³Õ<Ð<r7   c                óÎ   € \        V4      p\        P                  ! VR ,
          V4      V,
          \        P                  ! ^4      ,
          \        P
                  ! V4      ,
          # r8  )r	  r|   rµ  rQ   r  r  r¹  s   &&& r5   rý   Údgamma_gen._logpdf
  s?   € Ü�‹VˆÜ�xŠx˜˜C� Ó$ rÕ)¬B¯FªF°1«IÕ5¼¿
º
À1»ÕEÐEr7   c           	     ó´   € \         P                  ! V^ 8„  RR\        P                  ! W!4      ,          ,           R\        P                  ! W!) 4      ,          4      # ©r   r£   )rQ   r±  r|   rB  rF  r9  s   &&&r5   ry   Údgamma_gen._cdf  sB   € Ü�xŠx˜˜A™Ø˜c¤"§+¢+¨aÓ"3Õ3Õ3ØœBŸLšL¨¨BÓ/Õ/ó1ð 	1r7   c           
     ó´   € \         P                  ! V^ 8„  R\        P                  ! W!4      ,          RR\        P                  ! W!) 4      ,          ,           4      # r¿  )rQ   r±  r|   rF  rB  r9  s   &&&r5   r~   Údgamma_gen._sf  sB   € Ü�xŠx˜˜A™ØœBŸLšL¨Ó.Õ.Ø˜c¤"§+¢+¨a°Ó"4Õ4Õ4ó6ð 	6r7   c                óv   € \         P                  P                  V4      \        P                  ! R 4      ,
          # r  )rF  r(  r  rQ   r  rG  s   &&r5   r  Údgamma_gen._entropy  s$   € Ü�{‰{×#Ñ# AÓ&¬¯ª°«Õ4Ð4r7   c           	     ó¸   € \         P                  ! VR 8„  \        P                  ! V^V,          ^,
          4      \        P                  ! V^V,          4      ) 4      # r  ©rQ   r±  r|   rK  rP  rA  s   &&&r5   r„   Údgamma_gen._ppf  sD   € Ü�xŠx˜˜C™ÜŸš q¨!¨A­#°­'Ó2ÜŸš¨¨A¨a­CÓ0Ð0ó2ð 	2r7   c           	     ó¸   € \         P                  ! VR 8„  \        P                  ! V^V,          ^,
          4      ) \        P                  ! V^V,          4      4      # r  rÆ  rA  s   &&&r5   rˆ   Údgamma_gen._isf   sD   € Ü�xŠx˜˜C™ÜŸš¨¨1¨Q­3°­7Ó3Ð3ÜŸš¨¨1¨Q­3Ó/ó1ð 	1r7   c                ór   € WR ,           ,          pRVRVR,           VR,           ,          V,          R,
          3# )r–   r•   rÒ   r£  r‹   )rD   r˜   rz  s   && r5   r   Údgamma_gen._stats%  s2   € Ø�3•�iˆØ�C˜˜q �u q¨¥u�o¨cÕ1°#Õ5Ð5Ð5r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r~   r  r„   rˆ   r   r‘   r’   r“   s   @r5   r®  r®  Ý  sC   ø‡ € ñò>Eô.ò
=ò
Fò1ò
6ò
5ò2ò
1÷
6ð 6r7   r®  Údgammac                   ó   a € ] tR tRt o Rt]P                  t]P                  t	]P                  t]P                  t]P                  t]P                   tR tR tR tR tRR ltR	 tR
 tR t
R tR tR tR tRtV tR# )Údpareto_lognorm_geni-  añ  A double Pareto lognormal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `dpareto_lognorm` is:

.. math::

    f(x, \mu, \sigma, \alpha, \beta) =
    \frac{\alpha \beta}{(\alpha + \beta) x}
    \phi\left( \frac{\log x - \mu}{\sigma} \right)
    \left( R(y_1) + R(y_2) \right)

where :math:`R(t) = \frac{1 - \Phi(t)}{\phi(t)}`,
:math:`\phi` and :math:`\Phi` are the normal PDF and CDF, respectively,
:math:`y_1 = \alpha \sigma - \frac{\log x - \mu}{\sigma}`,
and :math:`y_2 = \beta \sigma + \frac{\log x - \mu}{\sigma}`
for real numbers :math:`x` and :math:`\mu`, :math:`\sigma > 0`,
:math:`\alpha > 0`, and :math:`\beta > 0` [1]_.

`dpareto_lognorm` takes
``u`` as a shape parameter for :math:`\mu`,
``s`` as a shape parameter for :math:`\sigma`,
``a`` as a shape parameter for :math:`\alpha`, and
``b`` as a shape parameter for :math:`\beta`.

A random variable :math:`X` distributed according to the PDF above
can be represented as :math:`X = U \frac{V_1}{V_2}` where :math:`U`,
:math:`V_1`, and :math:`V_2` are independent, :math:`U` is lognormally
distributed such that :math:`\log U \sim N(\mu, \sigma^2)`, and
:math:`V_1` and :math:`V_2` follow Pareto distributions with parameters
:math:`\alpha` and :math:`\beta`, respectively [2]_.

%(after_notes)s

References
----------
.. [1] Hajargasht, Gholamreza, and William E. Griffiths. "Pareto-lognormal
       distributions: Inequality, poverty, and estimation from grouped income
       data." Economic Modelling 33 (2013): 593-604.
.. [2] Reed, William J., and Murray Jorgensen. "The double Pareto-lognormal
       distribution - a new parametric model for size distributions."
       Communications in Statistics - Theory and Methods 33.8 (2004): 1733-1753.

%(example)s

c                óP   € V P                  V4      V P                  V4      ,          # rO   )Ú_PhicÚ_phi©rD   Úzs   &&r5   Ú_RÚdpareto_lognorm_gen._Rf  s   € Ø�z‰z˜!‹}˜tŸy™y¨›|Õ+Ð+r7   c                óP   € V P                  V4      V P                  V4      ,
          # rO   )Ú_logPhicÚ_logphirÒ  s   &&r5   Ú_logRÚdpareto_lognorm_gen._logRi  s   € Ø�}‰}˜QÓ $§,¡,¨q£/Õ1Ð1r7   c           	     ó  € \        R R\        P                  ) \        P                  3R4      \        RR^ \        P                  3R4      \        RR^ \        P                  3R4      \        RR^ \        P                  3R4      .# )rµ  Frj  r˜   r™   r4  rj   rl   s   &r5   rm   Údpareto_lognorm_gen._shape_infol  sm   € Ü˜3 ¬¯©¨´·±Ð'8¸.ÓIÜ˜3 ¨¬2¯6©6 {°NÓCÜ˜3 ¨¬2¯6©6 {°NÓCÜ˜3 ¨¬2¯6©6 {°NÓCðEð 	Er7   c                ó4   € V^ 8„  V^ 8„  ,          V^ 8„  ,          # r  r‹   )rD   rµ  rj  r˜   r™   s   &&&&&r5   rd   Údpareto_lognorm_gen._argcheckr  s   € Ø�A‘˜!˜a™%Õ  A¨¡EÕ*Ð*r7   Nc                óÐ   € VP                  WVR 7      pVP                  VR 7      pVP                  VR 7      p	\        P                  ! WxV,          ,           W”,          ,
          4      # ©r³  )ÚnormalÚstandard_exponentialrQ   rÓ   )
rD   rµ  rj  r˜   r™   rô   rõ   ÚZÚE1ÚE2s
   &&&&&&&   r5   rö   Údpareto_lognorm_gen._rvsu  s[   € ð ×Ñ ¨4ÐÓ0ˆØ×.Ñ.°DÐ.Ó9ˆØ×.Ñ.°DÐ.Ó9ˆÜ�vŠv�a˜q�&•j 2¥6Õ)Ó*Ð*r7   c           	     óø  € \         P                  ! R R R7      ;_uu_ 4        \         P                  ! V4      TrvWg,
          V,          pWC,          V,
          p	WS,          V,           p
\         P                  ! \         P                  ! V4      \         P                  ! V4      ,           \         P                  ! WE,           4      ,
          V,
          4      pW°P	                  V4      ,          pV\         P
                  ! V P                  V	4      V P                  V
4      4      ,          pRRR4       \         P                  ) XV^ 8H  \         P                  ! V4      ,          &   VR,          #   + '       g   i     LK; i)rl  ©Úinvalidrn  Nr‹   )	rQ   ro  r  r#  rØ  Ú	logaddexprÙ  rk   rW   )rD   rt   rµ  rj  r˜   r™   Úlog_yÚmrÓ  Úx1Úx2rJ  s   &&&&&&      r5   rý   Údpareto_lognorm_gen._logpdf~  sé   € Ü�[Š[ °(×;Ö;Ü—v’v˜a“y !�1Ø•˜a•ˆAØ•˜•ˆBØ•˜•ˆBÜ—*’*œRŸVšV A›Y¬¯ª°«Õ2´R·V²V¸A½E³]ÕBÀUÕJÓKˆCØ—<‘< “?Õ"ˆCØ”2—<’< §
¡
¨2£°·
±
¸2³Ó?Õ?ˆC÷ <ô (*§v¡v gˆˆQ�!‰V”r—x’x “{Õ"Ñ#Ø�2�wˆ÷ <×;ús   ¡DE)Å)E9	c           
     óp  € \         P                  ! R R R7      ;_uu_ 4        \         P                  ! V4      TrvWg,
          V,          pWC,          V,
          p	WS,          V,           p
V P                  V4      pV P	                  V4      p\         P                  ! V4      V P                  V	4      ,           p\         P                  ! V4      V P                  V
4      ,           p\         P                  ! W¼WÞ^4      w  r¼rÞp\        P                  ! WÞ.Wÿ) .^ RR7      w  ppW¼V,           \         P                  ! WE,           4      ,
          .p\         P                  ! \        P                  ! VWÿ) V,          .^ R7      4      pRRR4       \         P                  ) XV^ 8H  &   VR,          #   + '       g   i     L0; i)rl  rè  T)r™   rP  Úreturn_sign)r™   rP  Nr‹   )rQ   ro  r  Ú_logPhirØ  rÙ  rE  r|   Ú	logsumexpr#  rk   )rD   rt   rµ  rj  r˜   r™   rë  rì  rÓ  rí  rî  rû  rü  rý  Út4ÚoneÚt5rR   ÚtemprJ  s   &&&&&&              r5   r  Údpareto_lognorm_gen._logcdfŠ  s8  € Ü�[Š[ °(×;Ö;Ü—v’v˜a“y !�1Ø•˜a•ˆAØ•˜•ˆBØ•˜•ˆBØ—‘˜a“ˆBØ—‘˜a“ˆBÜ—&’&˜“)˜dŸj™j¨›nÕ,ˆBÜ—&’&˜“)˜dŸj™j¨›nÕ,ˆBÜ"$×"5Ò"5°b¸bÀaÓ"HÑˆB�B˜Cô Ÿš b X°#°t°À1ÐRVÔW‰HˆB�Ø˜R�¤"§&¢&¨­£-Õ/Ð0ˆDÜ—*’*œRŸ\š\¨$°3¸¸T½	Ð2BÈÔKÓLˆC÷ <ô  —v‘v�gˆˆA�‰F‰Ø�2�wˆ÷# <×;ús   ¡EF%Æ%F5	c           	     óP   € \         P                  ! V P                  WW4V4      4      # rO   )rq   Ú	_log1mexpr  ©rD   rt   rµ  rj  r˜   r™   s   &&&&&&r5   r
  Údpareto_lognorm_gen._logsfž  s   € Ü�}Š}˜TŸ\™\¨!°°aÓ8Ó9Ð9r7   c           	     óP   € \         P                  ! V P                  WW4V4      4      # rO   r.  rû  s   &&&&&&r5   ru   Údpareto_lognorm_gen._pdf£  ó   € Ü�vŠv�d—l‘l 1¨¨qÓ1Ó2Ð2r7   c           	     óP   € \         P                  ! V P                  WW4V4      4      # rO   ©rQ   rÓ   r  rû  s   &&&&&&r5   ry   Údpareto_lognorm_gen._cdf¦  rÿ  r7   c           	     óP   € \         P                  ! V P                  WW4V4      4      # rO   r“  rû  s   &&&&&&r5   r~   Údpareto_lognorm_gen._sf©  s   € Ü�vŠv�d—k‘k !¨¨aÓ0Ó1Ð1r7   c                ó@  € T\        V4      rvWE,          WG,
          WW,           ,          ,          \        P                  ! Wv,          V^,          V^,          ,          ^,          ,           4      ,          p\        P                  ! V4      p\        P                  W„V8*  &   V# rD  )ÚfloatrQ   rÓ   r#  rF  )	rD   rc   rµ  rj  r˜   r™   rì  rk  rJ  s	   &&&&&&   r5   r,  Údpareto_lognorm_gen._munp¬  si   € Ø”%˜“(ˆ1Ø�u˜!�% A¥EÕ*Õ+¬b¯fªf°QµU¸QÀ!½VÀaÈ1Åf½_ÈqÕ=PÕ5PÓ.QÕQˆÜ�jŠj˜‹oˆÜ—f‘fˆ�‰F‰Øˆ
r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r/  rý   rØ  r  rò  r
  r×  ru   rÑ  ry   Ú_Phir~   rÐ  rÔ  rÙ  rm   rd   rö   r,  r‘   r’   r“   s   @r5   rÎ  rÎ  -  s…   ø‡ € ñ0ðb �l‰l€GØ�l‰l€GØ�{‰{€HØ�9‰9€DØ�9‰9€DØ�H‰H€Eò,ò2òEò+ô+ò
òò(:ò
3ò3ò2÷ð r7   rÎ  Údpareto_lognormc                   ój   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tR tRtV tR# )Údweibull_geni·  aJ  A double Weibull continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `dweibull` is given by

.. math::

    f(x, c) = c / 2 |x|^{c-1} \exp(-|x|^c)

for a real number :math:`x` and :math:`c > 0`.

`dweibull` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Údweibull_gen._shape_infoÍ  r6  r7   Nc                ó˜   € VP                  VR 7      p\        P                  WVR7      pV\        P                  ! VR8¬  ^R4      ,          # r²  )r´  Úweibull_minr)  rQ   r±  )rD   r\  rô   rõ   rµ  Úws   &&&&  r5   rö   Údweibull_gen._rvsÐ  sC   € Ø× Ñ  dÐ Ó+ˆÜ�O‰O˜A°|ˆOÓDˆØ”B—H’H˜Q #™X q¨"Ó-Õ.Ð.r7   c                óš   € \        V4      pVR ,          W2R,
          ,          ,          \        P                  ! W2,          ) 4      ,          pV# ©rÒ   r–   )r	  rQ   rÓ   )rD   rt   r\  rº  ÚPxs   &&&  r5   ru   Údweibull_gen._pdfÕ  s5   € ä�‹VˆØ��W�r˜c�E•{Õ"¤R§V¢V¨R­U¨F£^Õ3ˆØˆ	r7   c                óÚ   € \        V4      p\        P                  ! V4      \        P                  ! R 4      ,
          \        P                  ! VR,
          V4      ,           W2,          ,
          # r  )r	  rQ   r  r|   rµ  )rD   rt   r\  rº  s   &&& r5   rý   Údweibull_gen._logpdfÛ  sA   € Ü�‹VˆÜ�vŠv�a‹yœ2Ÿ6š6 #›;Õ&¬¯ª°!°cµ'¸2Ó)>Õ>ÀÅÕFÐFr7   c                ó¢   € R \         P                  ! \        V4      V,          ) 4      ,          p\         P                  ! V^ 8„  ^V,
          V4      # r  )rQ   rÓ   r	  r±  )rD   rt   r\  ÚCx1s   &&& r5   ry   Údweibull_gen._cdfß  s:   € Ø”B—F’FœC ›F A�I˜:Ó&Õ&ˆÜ�xŠx˜˜A™˜q 3�w¨Ó,Ð,r7   c                óð   € R \         P                  ! VR8*  VRV,
          4      ,          p\         P                  ! \         P                  ! V4      ) RV,          4      p\         P                  ! VR8„  W3) 4      # ©rÒ   r£   r–   )rQ   r±  rU  r  )rD   rƒ   r\  rî  s   &&& r5   r„   Údweibull_gen._ppfã  sV   € Ø”2—8’8˜A ™H a¨¨a­Ó0Õ0ˆÜ�hŠhœŸš˜s›�| S¨1¥WÓ-ˆÜ�xŠx˜˜C™  dÓ+Ð+r7   c                ó¼   € R \         P                  P                  \        P                  ! V4      V4      ,          p\        P
                  ! V^ 8„  V^V,
          4      # r  )rF  r  r~   rQ   r	  r±  )rD   rt   r\  Úhalf_weibull_min_sfs   &&& r5   r~   Údweibull_gen._sfè  sF   € Ø!¤E×$5Ñ$5×$9Ñ$9¼"¿&º&À»)ÀQÓ$GÕGÐÜ�xŠx˜˜A™Ð2°AÐ8KÕ4KÓLÐLr7   c                óÊ   € R \         P                  ! VR8*  VRV,
          4      ,          p\        P                  P	                  W24      p\         P                  ! VR8„  V) V4      # r  )rQ   r±  rF  r  rˆ   )rD   rƒ   r\  Údouble_qÚweibull_min_isfs   &&&  r5   rˆ   Údweibull_gen._isfì  sQ   € ØœŸš  c¡¨1¨b°1­fÓ5Õ5ˆÜ×+Ñ+×0Ñ0°Ó=ˆÜ�xŠx˜˜C™ /Ð!1°?ÓCÐCr7   c                ó‚   € ^V^,          ,
          \         P                  ! RRV,          V,          ,           4      ,          # ©rM   r–   ©r|   r(  rô  s   &&&r5   r,  Údweibull_gen._munpñ  s+   € Ø�Q˜•U•œrŸxšx¨¨c°A­g¸­kÕ(9Ó:Õ:Ð:r7   c                ó   € R# ©r   )r   Nr   Nr‹   r÷  s   &&r5   r   Údweibull_gen._stats÷  ó   € ØÐr7   c                óz   € \         P                  P                  V4      \        P                  ! R 4      ,
          pV# r  )rF  r  r  rQ   r  )rD   r\  r‰  s   && r5   r  Údweibull_gen._entropyú  s*   € Ü×Ñ×&Ñ& qÓ)¬B¯FªF°3«KÕ7ˆØˆr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r„   r~   rˆ   r,  r   r  r‘   r’   r“   s   @r5   r  r  ·  sJ   ø‡ € ñò*Eô/ò
òGò-ò,ò
MòDò
;ò ÷ð r7   r  Údweibullc                   ó”   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tR t]]! ]RR7      R 4       4       tRtV tR# )Ú	expon_geni  a	  An exponential continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `expon` is:

.. math::

    f(x) = \exp(-x)

for :math:`x \ge 0`.

%(after_notes)s

A common parameterization for `expon` is in terms of the rate parameter
``lambda``, such that ``pdf = lambda * exp(-lambda * x)``. This
parameterization corresponds to using ``scale = 1 / lambda``.

The exponential distribution is a special case of the gamma
distributions, with gamma shape parameter ``a = 1``.

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úexpon_gen._shape_info  r¼   r7   Nc                ó$   € VP                  V4      # rO   )râ  ró   s   &&&r5   rö   Úexpon_gen._rvs   s   € Ø×0Ñ0°Ó6Ð6r7   c                ó0   € \         P                  ! V) 4      # rO   ©rQ   rÓ   r¿   s   &&r5   ru   Úexpon_gen._pdf#  s   € ä�vŠv�q�b‹zÐr7   c                ó   € V) # rO   r‹   r¿   s   &&r5   rý   Úexpon_gen._logpdf'  ó	   € Øˆrˆ	r7   c                ó2   € \         P                  ! V) 4      ) # rO   ©r|   rf  r¿   s   &&r5   ry   Úexpon_gen._cdf*  ó   € Ü—’˜!˜“ˆ}Ðr7   c                ó2   € \         P                  ! V) 4      ) # rO   r_  rÉ   s   &&r5   r„   Úexpon_gen._ppf-  r?  r7   c                ó0   € \         P                  ! V) 4      # rO   r7  r¿   s   &&r5   r~   Úexpon_gen._sf0  s   € Ü�vŠv�q�b‹zÐr7   c                ó   € V) # rO   r‹   r¿   s   &&r5   r
  Úexpon_gen._logsf3  r;  r7   c                ó0   € \         P                  ! V4      ) # rO   rc  rÉ   s   &&r5   rˆ   Úexpon_gen._isf6  ó   € Ü—’�q“	ˆzÐr7   c                ó   € R# )r–   )r–   r–   rÒ   ç      @r‹   rl   s   &r5   r   Úexpon_gen._stats9  r  r7   c                ó   € R # r8  r‹   rl   s   &r5   r  Úexpon_gen._entropy<  ó   € Ùr7   zú        When `method='MLE'`,
        this function uses explicit formulas for the maximum likelihood
        estimation of the exponential distribution parameters, so the
        `optimizer`, `loc` and `scale` keyword arguments are
        ignored.

r  c                ó0  € \        V4      ^ 8”  d   \        R4      hVP                  RR4      pVP                  RR4      p\        V4       Ve   Ve   \	        R4      h\
        P                  ! V4      p\
        P                  ! V4      P                  4       '       g   \	        R4      hVP                  4       pVf   TpM$TpWg8  d   \        RV\
        P                  R7      hVf   VP                  4       V,
          pMTp\        V4      \        V4      3# )	r   úToo many arguments.r  Nr  r   r!  ÚexponrÛ  )rç  r3   r2   r6   r"  rQ   r#  r$  r%  Úminrƒ  rk   r&  r  )	rD   rE   rF   r4   r  r  Údata_minr-   r.   s	   &&*,     r5   rB   Úexpon_gen.fit?  sõ   € ô ˆt‹9�qŒ=ÜÐ1Ó2Ð2à�x‰x˜ Ó%ˆØ—‘˜( DÓ)ˆä$ TÔ*àÒ Ò 2äð )ó *ð *ô �zŠz˜$Óˆä�{Š{˜4Ó ×$Ñ$×&Ò&ÜÐCÓDÐDà—8‘8“:ˆàŠ<à‰CàˆCØŒ~ä" 7°$¼b¿f¹fÔEÐEàŠ>à—I‘I“K #Õ%‰EàˆEô �S‹zœ5 ›<Ð'Ð'r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r„   r~   r
  rˆ   r   r  rK   r
   r   rB   r‘   r’   r“   s   @r5   r1  r1    si   ø‡ € ñò4ô7òòòòòòòò"òð Ù ð 6ô ñ&(óó ö&(r7   r1  rQ  c                   óR   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tRtV tR# )Úexponnorm_genir  a€  An exponentially modified Normal continuous random variable.

Also known as the exponentially modified Gaussian distribution [1]_.

%(before_notes)s

Notes
-----
The probability density function for `exponnorm` is:

.. math::

    f(x, K) = \frac{1}{2K} \exp\left(\frac{1}{2 K^2} - x / K \right)
              \text{erfc}\left(-\frac{x - 1/K}{\sqrt{2}}\right)

where :math:`x` is a real number and :math:`K > 0`.

It can be thought of as the sum of a standard normal random variable
and an independent exponentially distributed random variable with rate
``1/K``.

%(after_notes)s

An alternative parameterization of this distribution (for example, in
the Wikipedia article [1]_) involves three parameters, :math:`\mu`,
:math:`\lambda` and :math:`\sigma`.

In the present parameterization this corresponds to having ``loc`` and
``scale`` equal to :math:`\mu` and :math:`\sigma`, respectively, and
shape parameter :math:`K = 1/(\sigma\lambda)`.

.. versionadded:: 0.16.0

References
----------
.. [1] Exponentially modified Gaussian distribution, Wikipedia,
       https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# )ÚKFr4  rj   rl   s   &r5   rm   Úexponnorm_gen._shape_infoœ  r6  r7   Nc                ód   € VP                  V4      V,          pVP                  V4      pWE,           # rO   )râ  rò   )rD   rX  rô   rõ   ÚexpvalÚgvals   &&&&  r5   rö   Úexponnorm_gen._rvsŸ  s/   € Ø×2Ñ2°4Ó8¸1Õ<ˆØ×+Ñ+¨DÓ1ˆØ�}Ðr7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  )rD   rt   rX  s   &&&r5   ru   Úexponnorm_gen._pdf¤  ó   € Ü�vŠv�d—l‘l 1Ó(Ó)Ð)r7   c                ó¨   € R V,          pVRV,          V,
          ,          pV\        W,
          4      ,           \        P                  ! V4      ,
          # r‘  ©rß   rQ   r  )rD   rt   rX  ÚinvKÚexpargs   &&&  r5   rý   Úexponnorm_gen._logpdf§  s<   € Ø�Q�wˆØ˜˜t� a�Õ(ˆØœ Q¥XÓ.Õ.´·²¸³Õ:Ð:r7   c                ó¾   € R V,          pVRV,          V,
          ,          pV\        W,
          4      ,           p\        V4      \        P                  ! V4      ,
          # r‘  ©rß   rÜ   rQ   rÓ   ©rD   rt   rX  rc  r[  Úlogprods   &&&   r5   ry   Úexponnorm_gen._cdf¬  sE   € Ø�Q�wˆØ˜˜t� a�Õ(ˆØœ<¨­Ó1Õ1ˆÜ˜‹|œbŸfšf W›oÕ-Ð-r7   c                óÀ   € R V,          pVRV,          V,
          ,          pV\        W,
          4      ,           p\        V) 4      \        P                  ! V4      ,           # r‘  rg  rh  s   &&&   r5   r~   Úexponnorm_gen._sf²  sG   € Ø�Q�wˆØ˜˜t� a�Õ(ˆØœ<¨­Ó1Õ1ˆÜ˜!˜‹}œrŸvšv g›Õ.Ð.r7   c                ó¤   € W,          pR V,           p^V^,          ,          VR,          ,          pRV,          V,          VR,          ,          pWWE3# )r–   rJ  rw  r<  r‹   )rD   rX  ÚK2ÚopK2ÚskwÚkrts   &&    r5   r   Úexponnorm_gen._stats¸  sI   € Ø�UˆØ�R�xˆØ�!�Q•$�h˜ �Õ%ˆØ�B�h˜�m˜d R�jÕ(ˆØ˜Ð Ð r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r~   r   r‘   r’   r“   s   @r5   rV  rV  r  s4   ø‡ € ñ(òREôò
*ò;ò
.ò/÷!ð !r7   rV  Ú	exponnormc                óV   € \         P                  ! \        P                  ! W4      4      # )a  
Compute (1 + x)**y - 1.

Uses expm1 and xlog1py to avoid loss of precision when
(1 + x)**y is close to 1.

Note that the inverse of this function with respect to x is
``_pow1pm1(x, 1/y)``.  That is, if

    t = _pow1pm1(x, y)

then

    x = _pow1pm1(t, 1/y)
)rQ   rf  r|   r´  ©rt   Úys   &&r5   Ú_pow1pm1rw  Ã  s   € ô  �8Š8”B—J’J˜qÓ$Ó%Ð%r7   c                   óN   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
tV tR# )Úexponweib_geniÖ  a@  An exponentiated Weibull continuous random variable.

%(before_notes)s

See Also
--------
weibull_min, numpy.random.Generator.weibull

Notes
-----
The probability density function for `exponweib` is:

.. math::

    f(x, a, c) = a c [1-\exp(-x^c)]^{a-1} \exp(-x^c) x^{c-1}

and its cumulative distribution function is:

.. math::

    F(x, a, c) = [1-\exp(-x^c)]^a

for :math:`x > 0`, :math:`a > 0`, :math:`c > 0`.

`exponweib` takes :math:`a` and :math:`c` as shape parameters:

* :math:`a` is the exponentiation parameter,
  with the special case :math:`a=1` corresponding to the
  (non-exponentiated) Weibull distribution `weibull_min`.
* :math:`c` is the shape parameter of the non-exponentiated Weibull law.

%(after_notes)s

References
----------
https://en.wikipedia.org/wiki/Exponentiated_Weibull_distribution

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# ©r˜   Fr\  r4  rj   ©rD   r£  ry  s   &  r5   rm   Úexponweib_gen._shape_infoÿ  r¦  r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  ©rD   rt   r˜   r\  s   &&&&r5   ru   Úexponweib_gen._pdf	  ó   € ô �vŠv�d—l‘l 1¨Ó+Ó,Ð,r7   c                óB  € W,          ) p\         P                  ! V4      ) p\        P                  ! V4      \        P                  ! V4      ,           \         P                  ! VR ,
          V4      ,           V,           \         P                  ! VR ,
          V4      ,           pV# r8  )r|   rf  rQ   r  rµ  )rD   rt   r˜   r\  ÚnegxcÚexm1cÚlogps   &&&&   r5   rý   Úexponweib_gen._logpdf		  sm   € Ø•�ˆÜ—’˜%“Ð ˆÜ—’�q“	œBŸFšF 1›IÕ%¬¯ª°°Sµ¸%Ó(@Õ@ØõÜŸš  S¥¨!Ó,õ-ˆàˆr7   c                óN   € \         P                  ! W,          ) 4      ) pWB,          # rO   r=  )rD   rt   r˜   r\  r„  s   &&&& r5   ry   Úexponweib_gen._cdf	  s   € Ü—’˜1�4˜%“Ð ˆØ�xˆr7   c                ó’   € \         P                  ! VR V,          ,          ) 4      ) \        P                  ! R V,          4      ,          # r8  )r|   ré  rQ   r#  )rD   rƒ   r˜   r\  s   &&&&r5   r„   Úexponweib_gen._ppf	  s0   € Ü—’˜1˜s 1�u�:˜+Ó&Ð&¬¯ª°C¸µEÓ):Õ:Ð:r7   c                óT   € \        \        P                  ! W,          ) 4      ) V4      ) # rO   )rw  rQ   rÓ   r  s   &&&&r5   r~   Úexponweib_gen._sf	  s    € Üœ"Ÿ&š& !¥$ ›-˜¨Ó+Ð+Ð+r7   c                ór   € \         P                  ! \        V) ^V,          4      ) 4      ) ^V,          ,          # r_   )rQ   r  rw  )rD   rH  r˜   r\  s   &&&&r5   rˆ   Úexponweib_gen._isf	  s-   € Ü—’œ 1 " a¨¥cÓ*Ð*Ó+Ð+¨q°­sÕ3Ð3r7   r‹   N©rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   rˆ   r‘   r’   r“   s   @r5   ry  ry  Ö  s3   ø‡ € ñ'òPò
-ò
òò;ò,÷4ð 4r7   ry  Ú	exponweibc                   óN   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
tV tR# )Úexponpow_geni!	  aC  An exponential power continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `exponpow` is:

.. math::

    f(x, b) = b x^{b-1} \exp(1 + x^b - \exp(x^b))

for :math:`x \ge 0`, :math:`b > 0`.  Note that this is a different
distribution from the exponential power distribution that is also known
under the names "generalized normal" or "generalized Gaussian".

`exponpow` takes ``b`` as a shape parameter for :math:`b`.

%(after_notes)s

References
----------
http://www.math.wm.edu/~leemis/chart/UDR/PDFs/Exponentialpower.pdf

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# ©r™   Fr4  rj   rl   s   &r5   rm   Úexponpow_gen._shape_info=	  r6  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  ©rD   rt   r™   s   &&&r5   ru   Úexponpow_gen._pdf@	  ó   € ä�vŠv�d—l‘l 1Ó(Ó)Ð)r7   c                óÚ   € W,          p^\         P                  ! V4      ,           \        P                  ! VR,
          V4      ,           V,           \         P                  ! V4      ,
          pV# r&  )rQ   r  r|   rµ  rÓ   )rD   rt   r™   ÚxbÚfs   &&&  r5   rý   Úexponpow_gen._logpdfD	  sE   € Ø�TˆØ”—’�q“	�MœBŸHšH Q¨¥W¨aÓ0Õ0°2Õ5¼¿º¸r»
ÕBˆØˆr7   c                óf   € \         P                  ! \         P                  ! W,          4      ) 4      ) # rO   r=  r—  s   &&&r5   ry   Úexponpow_gen._cdfI	  s    € Ü—’œ"Ÿ(š( 1¥4›.˜Ó)Ð)Ð)r7   c                ód   € \         P                  ! \        P                  ! W,          4      ) 4      # rO   ©rQ   rÓ   r|   rf  r—  s   &&&r5   r~   Úexponpow_gen._sfL	  s   € Ü�vŠv”r—x’x ¥“~�oÓ&Ð&r7   c                ót   € \         P                  ! \        P                  ! V4      ) 4      R V,          ,          # r8  ©r|   ré  rQ   r  r—  s   &&&r5   rˆ   Úexponpow_gen._isfO	  s$   € Ü—’œ"Ÿ&š& ›)˜Ó$¨¨1­Õ-Ð-r7   c                ó|   € \        \        P                  ! \        P                  ! V) 4      ) 4      R V,          4      # r8  ©Úpowr|   ré  ©rD   rƒ   r™   s   &&&r5   r„   Úexponpow_gen._ppfR	  s(   € Ü”2—8’8œRŸXšX q b›\˜MÓ*¨C°­EÓ2Ð2r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r~   rˆ   r„   r‘   r’   r“   s   @r5   r’  r’  !	  s3   ø‡ € ñò6Eò*òò
*ò'ò.÷3ð 3r7   r’  Úexponpowc                   óv   a € ] tR tRt o Rt]P                  tR tRR lt	R t
R tR tR	 tR
 tR tR tRtV tR# )Úfatiguelife_geniY	  aô  A fatigue-life (Birnbaum-Saunders) continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `fatiguelife` is:

.. math::

    f(x, c) = \frac{x+1}{2c\sqrt{2\pi x^3}} \exp(-\frac{(x-1)^2}{2x c^2})

for :math:`x >= 0` and :math:`c > 0`.

`fatiguelife` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

References
----------
.. [1] "Birnbaum-Saunders distribution",
       https://en.wikipedia.org/wiki/Birnbaum-Saunders_distribution

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úfatiguelife_gen._shape_infov	  r6  r7   Nc                óØ   € VP                  V4      pR V,          V,          pWU,          pR^V,          ,           ^V,          \        P                  ! ^V,           4      ,          ,           pV# r¢   )rò   rQ   r'  )rD   r\  rô   rõ   rÓ  rt   rî  Úts   &&&&    r5   rö   Úfatiguelife_gen._rvsy	  sR   € Ø×(Ñ(¨Ó.ˆØ��E�!�GˆØ�SˆØ�!�B•$�J˜˜1�œRŸWšW Q¨¥V›_Õ,Õ,ˆØˆr7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r`  s   &&&r5   ru   Úfatiguelife_gen._pdf€	  s   € ô �vŠv�d—l‘l 1Ó(Ó)Ð)r7   c                ó”  € \         P                  ! V^,           4      V^,
          ^,          RV,          V^,          ,          ,          ,
          \         P                  ! ^V,          4      ,
          R\         P                  ! ^\         P                  ,          4      ^\         P                  ! V4      ,          ,           ,          ,
          # ©rM   rÒ   r£   r  r`  s   &&&r5   rý   Úfatiguelife_gen._logpdf…	  ss   € Ü—’�q˜•s“˜q �s Q�h¨#¨a­%°°1µ­*Õ5Õ5¼¿º¸qÀ½s»ÕCØ”R—V’V˜AœbŸe™e�G“_ q¬¯ª°«¥{Õ2Õ3õ4ð 	5r7   c                ó    € \        R V,          \        P                  ! V4      R \        P                  ! V4      ,          ,
          ,          4      # r8  )rÜ   rQ   r'  r`  s   &&&r5   ry   Úfatiguelife_gen._cdf‰	  s/   € Ü˜˜q�¤B§G¢G¨A£J°´R·W²W¸Q³ZµÕ$?Õ@ÓAÐAr7   c                ó˜   € V\        V4      ,          pR V\        P                  ! V^,          ^,           4      ,           ^,          ,          # ©ç      Ð?©rã   rQ   r'  ©rD   rƒ   r\  Útmps   &&& r5   r„   Úfatiguelife_gen._ppfŒ	  s6   € Ø”)˜A“,ÕˆØ�sœRŸWšW S¨!¥V¨a¥ZÓ0Õ0°1Õ4Õ4Ð4r7   c                ó    € \        R V,          \        P                  ! V4      R \        P                  ! V4      ,          ,
          ,          4      # r8  )ræ   rQ   r'  r`  s   &&&r5   r~   Úfatiguelife_gen._sf�	  s/   € Ü˜˜a�¤2§7¢7¨1£:°´B·G²G¸A³JµÕ#>Õ?Ó@Ð@r7   c                óš   € V) \        V4      ,          pR V\        P                  ! V^,          ^,           4      ,           ^,          ,          # r»  r½  r¾  s   &&& r5   rˆ   Úfatiguelife_gen._isf“	  s8   € Øˆb”9˜Q“<ÕˆØ�sœRŸWšW S¨!¥V¨a¥ZÓ0Õ0°1Õ4Õ4Ð4r7   c                óD  € W,          pVR ,          R,           pRV,          R,           pW$,          R,          p^V,          ^V,          R,           ,          \         P                  ! VR4      ,          p^V,          ^]V,          R,           ,          VR ,          ,          pW5Wg3# )rÒ   r–   r§  r¬  rJ  rS  g      D@©rQ   rU  )rD   r\  Úc2ry  Údenrz  r{  r|  s   &&      r5   r   Úfatiguelife_gen._stats—	  s   € ð �SˆØ�#�X˜�^ˆØ�B�h˜�nˆØ�f�s�lˆØ��U�b˜•e˜c•kÕ"¤R§X¢X¨c°3Ó%7Õ7ˆØ��V�r˜"•u˜t•|Õ$ s¨C¥xÕ/ˆØ˜ˆÐr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   rö   ru   rý   ry   r„   r~   rˆ   r   r‘   r’   r“   s   @r5   r­  r­  Y	  sL   ø‡ € ñð4 "×4Ñ4€MòEôò*ò
5òBò5òAò5÷ð r7   r­  Úfatiguelifec                   óR   a € ] tR tRt o RtR tR tRR ltR tR t	R	 t
R
 tRtV tR# )Úfoldcauchy_geni©	  aG  A folded Cauchy continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `foldcauchy` is:

.. math::

    f(x, c) = \frac{1}{\pi (1+(x-c)^2)} + \frac{1}{\pi (1+(x+c)^2)}

for :math:`x \ge 0` and :math:`c \ge 0`.

`foldcauchy` takes ``c`` as a shape parameter for :math:`c`.

%(example)s

c                ó   € V^ 8¬  # r  r‹   r÷  s   &&r5   rd   Úfoldcauchy_gen._argcheck½	  ó   € Ø�A‰vˆr7   c                ó@   € \        R R^ \        P                  3R4      .# ©r\  Fri   rj   rl   s   &r5   rm   Úfoldcauchy_gen._shape_infoÀ	  ó   € Ü˜3 ¨¬2¯6©6 {°MÓBÐCÐCr7   Nc                óB   € \        \        P                  WVR 7      4      # )©r-   rô   rõ   )r	  r.  r)  ©rD   r\  rô   rõ   s   &&&&r5   rö   Úfoldcauchy_gen._rvsÃ	  s$   € Ü”6—:‘: !Ø+7ð ó 9ó :ð 	:r7   c                ó¸   € R \         P                  ,          R ^W,
          ^,          ,           ,          R ^W,           ^,          ,           ,          ,           ,          # r8  r`  r`  s   &&&r5   ru   Úfoldcauchy_gen._pdfÇ	  s8   € à”2—5‘5�y˜#˜q !¥#¨¥�zÕ*¨S°!°QµS¸1µHµ*Õ-=Õ=Õ>Ð>r7   c                ó´   € R \         P                  ,          \         P                  ! W,
          4      \         P                  ! W,           4      ,           ,          # r8  ©rQ   r  Úarctanr`  s   &&&r5   ry   Úfoldcauchy_gen._cdfË	  s.   € Ø”2—5‘5�yœ"Ÿ)š) A¥C›.¬2¯9ª9°QµS«>Õ9Õ:Ð:r7   c                óª   € \         P                  ! ^W,
          4      \         P                  ! ^W,           4      ,           \         P                  ,          # r_   r  r`  s   &&&r5   r~   Úfoldcauchy_gen._sfÎ	  s2   € ô
 —
’
˜1˜a�eÓ$¤r§z¢z°!°QµUÓ';Õ;¼R¿U¹UÕBÐBr7   c                ó~   € \         P                  \         P                  \         P                  \         P                  3# rO   rE  r÷  s   &&r5   r   Úfoldcauchy_gen._statsÕ	  r  r7   r‹   r.  ©rŒ   r�   rŽ   r�   r�   rd   rm   rö   ru   ry   r~   r   r‘   r’   r“   s   @r5   rÌ  rÌ  ©	  s4   ø‡ € ñò&òDô:ò?ò;òC÷.ð .r7   rÌ  Ú
foldcauchyc                   ó^   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tRtV tR# )Úf_geniÜ	  a�  An F continuous random variable.

For the noncentral F distribution, see `ncf`.

%(before_notes)s

See Also
--------
ncf

Notes
-----
The F distribution with :math:`df_1 > 0` and :math:`df_2 > 0` degrees of freedom is
the distribution of the ratio of two independent chi-squared distributions with
:math:`df_1` and :math:`df_2` degrees of freedom, after rescaling by
:math:`df_2 / df_1`.

The probability density function for `f` is:

.. math::

    f(x, df_1, df_2) = \frac{df_2^{df_2/2} df_1^{df_1/2} x^{df_1 / 2-1}}
                            {(df_2+df_1 x)^{(df_1+df_2)/2}
                             B(df_1/2, df_2/2)}

for :math:`x > 0`.

`f` accepts shape parameters ``dfn`` and ``dfd`` for :math:`df_1`, the degrees of
freedom of the chi-squared distribution in the numerator, and :math:`df_2`, the
degrees of freedom of the chi-squared distribution in the denominator, respectively.

%(after_notes)s

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# )ÚdfnFÚdfdr4  rj   )rD   ÚidfnÚidfds   &  r5   rm   Úf_gen._shape_info
  s:   € Ü˜% ¨¬B¯F©F¨°^ÓDˆÜ˜% ¨¬B¯F©F¨°^ÓDˆØˆ|Ðr7   Nc                ó&   € VP                  WV4      # rO   )rœ  )rD   rç  rè  rô   rõ   s   &&&&&r5   rö   Ú
f_gen._rvs
  s   € Ø�~‰~˜c¨Ó-Ð-r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  ©rD   rt   rç  rè  s   &&&&r5   ru   Ú
f_gen._pdf	
  s   € ô �vŠv�d—l‘l 1¨3Ó/Ó0Ð0r7   c                óä  € R V,          pR V,          pV^,          \         P                  ! V4      ,          V^,          \         P                  ! V4      ,          ,           \        P                  ! V^,          ^,
          V4      ,           WE,           ^,          \         P                  ! WTV,          ,           4      ,          \        P                  ! V^,          V^,          4      ,           ,
          pV# r8  )rQ   r  r|   rµ  r¶  )rD   rt   rç  rè  rc   rì  r·  s   &&&&   r5   rý   Úf_gen._logpdf
  s•   € Ø�#�IˆØ�#�IˆØ��s”R—V’V˜A“Y�  1¥¤r§v¢v¨a£y¥Õ0´2·8²8¸A¸a½CÀ!½GÀQÓ3GÕGØ•C˜•7œbŸfšf Q¨1­¥W›oÕ-´·	²	¸!¸A½#¸qÀ½sÓ0CÕCõEˆàˆ
r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Úfdtrrï  s   &&&&r5   ry   Ú
f_gen._cdf
  s   € Ü�wŠw�s Ó#Ð#r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Úfdtrcrï  s   &&&&r5   r~   Ú	f_gen._sf
  ó   € Ü�xŠx˜ !Ó$Ð$r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Úfdtri)rD   rƒ   rç  rè  s   &&&&r5   r„   Ú
f_gen._ppf
  rù  r7   c                ó0  € R V,          R V,          rCVR,
          VR,
          VR,
          VR,
          3w  rVrx\         P                  ! V^8„  WE3R \        P                  R7      p	\         P                  ! V^8„  W4WV3R \        P                  R7      p
\         P                  ! V^8„  W5Wg3R \        P                  R7      pV\        P
                  ! R4      ,          p\         P                  ! V^8„  W·V3R	 \        P                  R7      pVR
,          pWšW¼3# )r–   rÒ   r¬  rJ  ç       @c                 ó   € W,          # rO   r‹   )Úv2Úv2_2s   &&r5   r  Úf_gen._stats.<locals>.<lambda>%
  s   € ˜RžYr7   r  c                 ór   € ^V,          V,          W,           ,          W^,          ,          V,          ,          # rD  r‹   )Úv1r   r  Úv2_4s   &&&&r5   r  r  *
  s$   € Ø��F�R�K˜2�9Õ%¨°A­g­¸Õ)<Ö=r7   c                 óŒ   € ^V ,          V,           V,          \         P                  ! W W,           ,          ,          4      ,          # rD  rÇ  )r  r  r  Úv2_6s   &&&&r5   r  r  0
  s*   € Ø��V�d�]˜dÕ"¤R§W¢W¨T¸2½9Õ5EÕ-FÓ%GÖGr7   c                 ó<   € ^W ,          V,          ,           V,          # )é   r‹   )r{  r  Úv2_8s   &&&r5   r  r  7
  s   €  A¨­°$­Õ$6¸$Ö#>r7   rS  )r  r  rQ   rk   rF  r'  )rD   rç  rè  r  r   r  r  r  r
  ry  rz  r{  r|  s   &&&          r5   r   Úf_gen._stats
  sû   € Ø�c•˜2 �8ˆBØ!# b¥¨"¨r­'°2¸µ7¸BÀ½GÐ!CÑˆ�Dä�_Š_Ø�‰F�R�JÙ&Ü—v‘vôˆô
 �oŠoØ�‰F�R˜TÐ(ñ>ä—v‘vô	ˆô �_Š_Ø�‰F�R˜tÐ*ñHä—v‘vô	ˆð
 	Œb�gŠg�b‹kÕˆä�_Š_Ø�‰F�R˜tÐ$Ù>Ü—v‘vôˆð 	ˆg�ˆà˜ˆÐr7   c                óÄ  € R V,          pR V,          pR W,           ,          p\         P                  ! V4      \         P                  ! V4      ,
          \        P                  ! W44      ,           ^V,
          \        P                  ! V4      ,          ,           ^V,           \        P                  ! V4      ,          ,
          V\        P                  ! V4      ,          ,           # r  )rQ   r  r|   r¶  r•  )rD   rç  rè  Úhalf_dfnÚhalf_dfdÚhalf_sums   &&&   r5   r  Úf_gen._entropy=
  s›   € ð ˜•9ˆØ˜•9ˆØ˜#�)Õ$ˆä—’�s“œbŸfšf S›kÕ)¬B¯IªI°hÓ,IÕIØ�X•¤§¢¨Ó!1Õ1õ2Ø56¸µ\Ü—’�xÓ õ5!õ!à#+¬b¯fªf°XÓ.>Õ#>õ?ð 	@r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r~   r„   r   r  r‘   r’   r“   s   @r5   rå  rå  Ü	  s?   ø‡ € ñ#òHô
.ò1òò$ò%ò%ò÷<
@ð 
@r7   rå  rœ  c                   óR   a € ] tR tRt o RtR tR tRR ltR tR t	R	 t
R
 tRtV tR# )Úfoldnorm_geniU
  aN  A folded normal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `foldnorm` is:

.. math::

    f(x, c) = \sqrt{2/\pi} cosh(c x) \exp(-\frac{x^2+c^2}{2})

for :math:`x \ge 0` and :math:`c \ge 0`.

`foldnorm` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó   € V^ 8¬  # r  r‹   r÷  s   &&r5   rd   Úfoldnorm_gen._argcheckk
  rÏ  r7   c                ó@   € \        R R^ \        P                  3R4      .# rÑ  rj   rl   s   &r5   rm   Úfoldnorm_gen._shape_infon
  rÓ  r7   Nc                óD   € \        VP                  V4      V,           4      # rO   ©r	  rò   rÖ  s   &&&&r5   rö   Úfoldnorm_gen._rvsq
  s   € Ü�<×/Ñ/°Ó5¸Õ9Ó:Ð:r7   c                óP   € \        W,           4      \        W,
          4      ,           # rO   rù   r`  s   &&&r5   ru   Úfoldnorm_gen._pdft
  s   € ä˜�Ó¤)¨A­C£.Õ0Ð0r7   c                óÒ   € \         P                  ! ^4      pR\        P                  ! W,
          V,          4      \        P                  ! W,           V,          4      ,           ,          # rI  )rQ   r'  r|   Úerf)rD   rt   r\  Úsqrt_twos   &&& r5   ry   Úfoldnorm_gen._cdfx
  s?   € Ü—7’7˜1“:ˆØ”b—f’f˜a�e XÕ-Ó.´·²¸½ÀÕ8HÓ1IÕIÕJÐJr7   c                óP   € \        W,
          4      \        W,           4      ,           # rO   r  r`  s   &&&r5   r~   Úfoldnorm_gen._sf|
  s   € Ü˜�‹¤¨!­%£Õ0Ð0r7   c                óò  € W,          p\         P                  ! RV,          4      \         P                  ! R\         P                  ,          4      ,          pRV,          V\        P
                  ! V\         P                  ! ^4      ,          4      ,          ,           pV^,           WD,          ,
          pRWD,          V,          W$,          ,
          V,
          ,          pV\         P                  ! VR4      ,          pW"R,           ,          ^,           RV,          V,          ,           pVRVR,
          ,          RV^,          ,          ,
          V^,          ,          ,          pWuR,          ,          R,
          pWEWg3# )r£   rÒ   rS  rJ  rþ  r£  ç      à¿)rQ   rÓ   r'  r  r|   r  rU  )rD   r\  rÇ  Úexpfacry  rz  r{  r|  s   &&      r5   r   Úfoldnorm_gen._stats
  sù   € ð �SˆÜ—’˜˜R�“¤2§7¢7¨2¬b¯e©e­8Ó#4Õ4ˆà��Y˜œRŸVšV A¤b§g¢g¨a£j¥LÓ1Õ1Õ1ˆØ�1�f�r•u�nˆà�2•5˜•8˜b�eÕ# fÕ,Õ-ˆØ
Œb�hŠh�s˜CÓ Õ ˆà˜•7�^˜aÕ " V¥)¨B¥,Õ.ˆØ
ˆr�R˜"•W�~  R¨¥U¥
Õ*¨b°!­eÕ3Õ3ˆØ�s•(�]˜RÕˆà˜ˆÐr7   r‹   r.  râ  r“   s   @r5   r  r  U
  s4   ø‡ € ñò*òDô;ò1òKò1÷ð r7   r  Úfoldnormc                   óŒ   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 tR tR t]! ]RR7      V 3R l4       tRtVtV ;t# )Úweibull_min_geni–
  a‰  Weibull minimum continuous random variable.

The Weibull Minimum Extreme Value distribution, from extreme value theory
(Fisher-Gnedenko theorem), is also often simply called the Weibull
distribution. It arises as the limiting distribution of the rescaled
minimum of iid random variables.

%(before_notes)s

See Also
--------
weibull_max, numpy.random.Generator.weibull, exponweib

Notes
-----
The probability density function for `weibull_min` is:

.. math::

    f(x, c) = c x^{c-1} \exp(-x^c)

for :math:`x > 0`, :math:`c > 0`.

`weibull_min` takes ``c`` as a shape parameter for :math:`c`.
(named :math:`k` in Wikipedia article and :math:`a` in
``numpy.random.weibull``).  Special shape values are :math:`c=1` and
:math:`c=2` where Weibull distribution reduces to the `expon` and
`rayleigh` distributions respectively.

Suppose ``X`` is an exponentially distributed random variable with
scale ``s``. Then ``Y = X**k`` is `weibull_min` distributed with shape
``c = 1/k`` and scale ``s**k``.

%(after_notes)s

References
----------
https://en.wikipedia.org/wiki/Weibull_distribution

https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úweibull_min_gen._shape_infoÃ
  r6  r7   c                ó~   € V\        W^,
          4      ,          \        P                  ! \        W4      ) 4      ,          # r_   ©r¨  rQ   rÓ   r`  s   &&&r5   ru   Úweibull_min_gen._pdfÆ
  s(   € à”�Q˜!�“�}œRŸVšV¤S¨£Y JÓ/Õ/Ð/r7   c                ó”   € \         P                  ! V4      \        P                  ! V^,
          V4      ,           \	        W4      ,
          # r_   ©rQ   r  r|   rµ  r¨  r`  s   &&&r5   rý   Úweibull_min_gen._logpdfÊ
  s-   € Ü�vŠv�a‹yœ2Ÿ8š8 A¨¥E¨1Ó-Õ-´°A³	Õ9Ð9r7   c                óD   € \         P                  ! \        W4      ) 4      ) # rO   ©r|   rf  r¨  r`  s   &&&r5   ry   Úweibull_min_gen._cdfÍ
  s   € Ü—’œ#˜a›)˜Ó$Ð$Ð$r7   c                óT   € \        \        P                  ! V) 4      ) R V,          4      # r8  r§  rg  s   &&&r5   r„   Úweibull_min_gen._ppfÐ
  s   € Ü”B—H’H˜a˜R“L�= # a¥%Ó(Ð(r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r“  r`  s   &&&r5   r~   Úweibull_min_gen._sfÓ
  ó   € Ü�vŠv�d—k‘k !Ó'Ó(Ð(r7   c                ó   € \        W4      ) # rO   ©r¨  r`  s   &&&r5   r
  Úweibull_min_gen._logsfÖ
  s   € Ü�A“	ˆzÐr7   c                óL   € \         P                  ! V4      ) ^V,          ,          # r_   rc  rg  s   &&&r5   rˆ   Úweibull_min_gen._isfÙ
  s   € Ü—’˜“�
˜a �cÕ"Ð"r7   c                óX   € \         P                  ! R VR ,          V,          ,           4      # r8  r'  rô  s   &&&r5   r,  Úweibull_min_gen._munpÜ
  s   € Ü�xŠx˜˜A˜c�E !�G�Ó$Ð$r7   c                óx   € \         ) V,          \        P                  ! V4      ,
          \         ,           ^,           # r_   ©r#   rQ   r  r÷  s   &&r5   r  Úweibull_min_gen._entropyß
  ó%   € Üˆw˜�{œRŸVšV A›YÕ&¬Õ/°!Õ3Ð3r7   aÌ          If ``method='mm'``, parameters fixed by the user are respected, and the
        remaining parameters are used to match distribution and sample moments
        where possible. For example, if the user fixes the location with
        ``floc``, the parameters will only match the distribution skewness and
        variance to the sample skewness and variance; no attempt will be made
        to match the means or minimize a norm of the errors.
        

r  c           	     ó
  <aa€ \        V\        4      '       d;   VP                  4       ^ 8X  d   VP                  4       pM\        SV `  ! V.VO5/ VB # VP                  RR4      '       d   \        SV `  ! V.VO5/ VB # \        WW#4      w  rrVVP                  RR4      P                  4       pR o\        P                  ! V4      oRpS! V4      p	SV	8  d(   VR8w  d!   Vf   V'       g   \        SV `  ! V.VO5/ VB # VR8X  d   RRRrËp
M@\        V4      '       d
   V^ ,          MRp
VP                  R	R4      pVP                  R
R4      pVf%   V
f!   \        VV3R lRV.RR7      P                  p
MVe   Tp
Vf‹   Vf‡   \        P                   ! V4      p\        P"                  ! V\$        P&                  ! ^^V
,          ,           4      \$        P&                  ! ^^V
,          ,           4      ^,          ,
          ,          4      pMVe   TpVfM   VfI   \        P(                  ! V4      pWì\$        P&                  ! ^^V
,          ,           4      ,          ,
          pMVe   TpVR8X  d   W«V3# \        SV `  ! W3R	VR
V/VB # )r   ÚsuperfitFr0   r:   c                 ón  € \         P                  ! ^^V ,          ,           4      p\         P                  ! ^^V ,          ,           4      p\         P                  ! ^^V ,          ,           4      p^V^,          ,          ^V,          V,          ,
          V,           pW!^,          ,
          R,          pWE,          # ©rM   rS  r'  )r\  Úgamma1Úgamma2Úgamma3ÚnumrÈ  s   &     r5   ÚskewÚ!weibull_min_gen.fit.<locals>.skewý
  sx   € Ü—X’X˜a  !¥�e“_ˆFÜ—X’X˜a  !¥�e“_ˆFÜ—X’X˜a  !¥�e“_ˆFØ�f˜a•i•- ! F¥(¨6¥/Õ1°FÕ:ˆCØ A�IÕ%¨Õ-ˆCØ•7ˆNr7   g     ˆÃ@r;   Nr-   r.   c                 ó"   <€ S! V 4      S,
          # rO   r‹   )r\  rj  rL  s   &€€r5   r  Ú%weibull_min_gen.fit.<locals>.<lambda>  s   ø€ ¡d¨1£g°¦kr7   g{®Gáz”?Úbisect)Úbracketr0   )r>   r)   r?   rÕ  r@   rB   r2   Ú_check_fit_input_parametersr<   r=   rF  rL  rç  r*   ÚrootrQ   rê  r'  r|   r(  r&  )rD   rE   rF   r4   Úfcr  r  r0   Úmax_cÚs_minr\  r-   r.   r  rì  rj  rL  rØ  s   &&*,           @@€r5   rB   Úweibull_min_gen.fitâ
  s;  ú€ ô �dœL×)Ò)Ø× Ñ Ó" aÔ'Ø—~‘~Ó'‘ä‘w’{ 4Ð7¨$Ò7°$Ñ7Ð7à�8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ô "=¸TØ=Aó"IÑˆ�$à—‘˜( EÓ*×0Ñ0Ó2ˆò	ô �JŠJ�tÓˆØˆÙ�U“ˆØˆuŒ9˜ 4œ¨BªJ¿tÜ‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ð �TŒ>Ø  $¨�EˆA�Eä˜tŸ9š9��Q–¨$ˆAØ—(‘(˜5 $Ó'ˆCØ—H‘H˜W dÓ+ˆEàŠ:˜!š)ô Õ1¸DÀ%¸=Ø#+ô-ß-1©Tñ àŠ^ØˆAàŠ>˜ešmÜ—’�t“ˆAÜ—G’G˜A¤§¢¨!¨A¨a­C­%£´2·8²8¸A¸aÀ½c½E³?ÀAÕ3EÕ!EÕFÓG‰EØÒØˆEàŠ<˜CšKÜ—’˜“ˆAØœBŸHšH Q¨¨1­¥WÓ-Õ-Õ-‰CØÒØˆCà�TŒ>Ø˜5�=Ð ô ‘7’;˜tÑE¨CÐE°uÐEÀÑEÐEr7   r‹   )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   r
  rˆ   r,  r  r	   r   rB   r‘   r’   r  r   s   @@r5   r(  r(  –
  si   ù‡ € ñ+òXEò0ò:ò%ò)ò)òò#ò%ò4ñ ˜}ð 5ô ôJFó÷JFð JFr7   r(  r  c                   ó~   a a€ ] tR tRt oRtR tR tV 3R ltR tR t	R t
R	 tR
 tR tR tR tR tR tRtVtV ;t# )Útruncweibull_min_geni:  aÍ  A doubly truncated Weibull minimum continuous random variable.

%(before_notes)s

See Also
--------
weibull_min, truncexpon

Notes
-----
The probability density function for `truncweibull_min` is:

.. math::

    f(x, a, b, c) = \frac{c x^{c-1} \exp(-x^c)}{\exp(-a^c) - \exp(-b^c)}

for :math:`a < x <= b`, :math:`0 \le a < b` and :math:`c > 0`.

`truncweibull_min` takes :math:`a`, :math:`b`, and :math:`c` as shape
parameters.

Notice that the truncation values, :math:`a` and :math:`b`, are defined in
standardized form:

.. math::

    a = (u_l - loc)/scale
    b = (u_r - loc)/scale

where :math:`u_l` and :math:`u_r` are the specific left and right
truncation values, respectively. In other words, the support of the
distribution becomes :math:`(a*scale + loc) < x <= (b*scale + loc)` when
:math:`loc` and/or :math:`scale` are provided.

%(after_notes)s

References
----------

.. [1] Rinne, H. "The Weibull Distribution: A Handbook". CRC Press (2009).

%(example)s

c                ó2   € VR 8¬  W28„  ,          VR 8„  ,          # ©r•   r‹   ©rD   r\  r˜   r™   s   &&&&r5   rd   Útruncweibull_min_gen._argcheckg  s   € Ø�R‘˜A™EÕ" a¨"¡fÕ-Ð-r7   c                ó¾   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      p\        RR^ \        P                  3R4      pWV.# )r\  Fr˜   r™   r4  ri   rj   )rD   ry  r£  r¤  s   &   r5   rm   Ú truncweibull_min_gen._shape_infoj  sT   € Ü˜˜U Q¬¯© K°Ó@ˆÜ˜˜U Q¬¯© K°Ó?ˆÜ˜˜U Q¬¯© K°Ó@ˆØ˜ˆ|Ðr7   c                ó&   <€ \         SV `  VRR7      # )rM   r…  )rM   r   rM   ©r@   r×  ©rD   rE   rØ  s   &&€r5   r×  Útruncweibull_min_gen._fitstartp  s   ø€ ä‰wÑ  ¨IÐ Ó6Ð6r7   c                ó   € W#3# rO   r‹   r\  s   &&&&r5   r¥   Ú!truncweibull_min_gen._get_supportt  ó	   € Øˆtˆr7   c                ó  € \         P                  ! \        W24      ) 4      \         P                  ! \        WB4      ) 4      ,
          pV\        W^,
          4      ,          \         P                  ! \        W4      ) 4      ,          V,          # r_   ©rQ   rÓ   r¨  )rD   rt   r\  r˜   r™   Údenums   &&&&& r5   ru   Útruncweibull_min_gen._pdfw  sU   € Ü—’œ˜Q›˜
Ó#¤b§f¢f¬c°!«i¨ZÓ&8Õ8ˆØ”C˜˜Q�3“K•¤"§&¢&¬#¨a«)¨Ó"4Õ4¸Õ=Ð=r7   c           	     óT  € \         P                  ! \         P                  ! \        W24      ) 4      \         P                  ! \        WB4      ) 4      ,
          4      p\         P                  ! V4      \        P
                  ! V^,
          V4      ,           \        W4      ,
          V,
          # r_   )rQ   r  rÓ   r¨  r|   rµ  )rD   rt   r\  r˜   r™   Úlogdenums   &&&&& r5   rý   Útruncweibull_min_gen._logpdf{  sc   € Ü—6’6œ"Ÿ&š&¤# a£) Ó,¬r¯vªv´s¸1³y°jÓ/AÕAÓBˆÜ�vŠv�a‹yœ2Ÿ8š8 A¨¥E¨1Ó-Õ-´°A³	Õ9¸HÕDÐDr7   c                ó&  € \         P                  ! \        W24      ) 4      \         P                  ! \        W4      ) 4      ,
          p\         P                  ! \        W24      ) 4      \         P                  ! \        WB4      ) 4      ,
          pWV,          # rO   rh  ©rD   rt   r\  r˜   r™   rK  ri  s   &&&&&  r5   ry   Útruncweibull_min_gen._cdf  óZ   € Ü�vŠv”s˜1“y�jÓ!¤B§F¢F¬C°«I¨:Ó$6Õ6ˆÜ—’œ˜Q›˜
Ó#¤b§f¢f¬c°!«i¨ZÓ&8Õ8ˆØ�{Ðr7   c           	     óv  € \         P                  ! \         P                  ! \        W24      ) 4      \         P                  ! \        W4      ) 4      ,
          4      p\         P                  ! \         P                  ! \        W24      ) 4      \         P                  ! \        WB4      ) 4      ,
          4      pWV,
          # rO   ©rQ   r  rÓ   r¨  ©rD   rt   r\  r˜   r™   Úlognumrl  s   &&&&&  r5   r  Útruncweibull_min_gen._logcdf„  óm   € Ü—’œŸš¤ A£	˜zÓ*¬R¯VªV´S¸³Y°JÓ-?Õ?Ó@ˆÜ—6’6œ"Ÿ&š&¤# a£) Ó,¬r¯vªv´s¸1³y°jÓ/AÕAÓBˆØÕ Ð r7   c                ó&  € \         P                  ! \        W4      ) 4      \         P                  ! \        WB4      ) 4      ,
          p\         P                  ! \        W24      ) 4      \         P                  ! \        WB4      ) 4      ,
          pWV,          # rO   rh  ro  s   &&&&&  r5   r~   Útruncweibull_min_gen._sf‰  rq  r7   c           	     óv  € \         P                  ! \         P                  ! \        W4      ) 4      \         P                  ! \        WB4      ) 4      ,
          4      p\         P                  ! \         P                  ! \        W24      ) 4      \         P                  ! \        WB4      ) 4      ,
          4      pWV,
          # rO   rs  rt  s   &&&&&  r5   r
  Útruncweibull_min_gen._logsfŽ  rw  r7   c                ó  € \        \        P                  ! ^V,
          \        P                  ! \        WB4      ) 4      ,          V\        P                  ! \        W24      ) 4      ,          ,           4      ) ^V,          4      # r_   ©r¨  rQ   r  rÓ   ©rD   rƒ   r\  r˜   r™   s   &&&&&r5   rˆ   Útruncweibull_min_gen._isf“  óU   € ÜÜ�VŠV�Q˜•UœbŸfšf¤c¨!£i ZÓ0Õ0°1´r·v²v¼sÀ1»y¸jÓ7IÕ3IÕIÓJÐJÈAÈaÍCóð 	r7   c                ó  € \        \        P                  ! ^V,
          \        P                  ! \        W24      ) 4      ,          V\        P                  ! \        WB4      ) 4      ,          ,           4      ) ^V,          4      # r_   r}  r~  s   &&&&&r5   r„   Útruncweibull_min_gen._ppf˜  r€  r7   c           	     óª  € \         P                  ! W,          R ,           4      \         P                  ! W,          R ,           \        WB4      4      \         P                  ! W,          R ,           \        W24      4      ,
          ,          p\        P
                  ! \        W24      ) 4      \        P
                  ! \        WB4      ) 4      ,
          pWV,          # r8  )r|   r(  rB  r¨  rQ   rÓ   )rD   rc   r\  r˜   r™   Ú	gamma_funri  s   &&&&&  r5   r,  Útruncweibull_min_gen._munp�  s€   € Ü—H’H˜Q�S 2�XÓ&Ü�KŠK˜�˜b�¤# a£)Ó,¬r¯{ª{¸1½3À½8ÄSÈÃYÓ/OÕOõˆ	ô —’œ˜Q›˜
Ó#¤b§f¢f¬c°!«i¨ZÓ&8Õ8ˆØÕ Ð r7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   r×  r¥   ru   rý   ry   r  r~   r
  rˆ   r„   r,  r‘   r’   r  r   s   @@r5   rY  rY  :  sR   ù‡ € ñ+òX.òõ7òò>òEòò
!ò
ò
!ò
ò
÷
!ò !r7   rY  Útruncweibull_minc                   óZ   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tRtV tR# )Úweibull_max_geni©  aØ  Weibull maximum continuous random variable.

The Weibull Maximum Extreme Value distribution, from extreme value theory
(Fisher-Gnedenko theorem), is the limiting distribution of rescaled
maximum of iid random variables. This is the distribution of -X
if X is from the `weibull_min` function.

%(before_notes)s

See Also
--------
weibull_min

Notes
-----
The probability density function for `weibull_max` is:

.. math::

    f(x, c) = c (-x)^{c-1} \exp(-(-x)^c)

for :math:`x < 0`, :math:`c > 0`.

`weibull_max` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

References
----------
https://en.wikipedia.org/wiki/Weibull_distribution

https://en.wikipedia.org/wiki/Fisher-Tippett-Gnedenko_theorem

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úweibull_max_gen._shape_infoÎ  r6  r7   c                ó†   € V\        V) V^,
          4      ,          \        P                  ! \        V) V4      ) 4      ,          # r_   r,  r`  s   &&&r5   ru   Úweibull_max_gen._pdfÑ  s0   € à”�a�R˜˜1�“�~œbŸfšf¤c¨1¨"¨a£j [Ó1Õ1Ð1r7   c                óš   € \         P                  ! V4      \        P                  ! V^,
          V) 4      ,           \	        V) V4      ,
          # r_   r/  r`  s   &&&r5   rý   Úweibull_max_gen._logpdfÕ  s3   € Ü�vŠv�a‹yœ2Ÿ8š8 A a¥C¨!¨Ó,Õ,¬s°A°2°q«zÕ9Ð9r7   c                óF   € \         P                  ! \        V) V4      ) 4      # rO   rh  r`  s   &&&r5   ry   Úweibull_max_gen._cdfØ  s   € Ü�vŠv”s˜A˜2˜q“z�kÓ"Ð"r7   c                ó   € \        V) V4      ) # rO   r:  r`  s   &&&r5   r  Úweibull_max_gen._logcdfÛ  s   € Ü�Q�B˜“
ˆ{Ðr7   c                óH   € \         P                  ! \        V) V4      ) 4      ) # rO   r2  r`  s   &&&r5   r~   Úweibull_max_gen._sfÞ  s   € Ü—’œ#˜q˜b !›*˜Ó%Ð%Ð%r7   c                óT   € \        \        P                  ! V4      ) R V,          4      ) # r8  )r¨  rQ   r  rg  s   &&&r5   r„   Úweibull_max_gen._ppfá  s    € Ü”R—V’V˜A“Y�J  A¥Ó&Ð&Ð&r7   c                ó°   € \         P                  ! R VR ,          V,          ,           4      p\        V4      ^,          '       d   RpWC,          # ^pWC,          # )r–   r  )r|   r(  r+  )rD   rc   r\  ÚvalÚsgns   &&&  r5   r,  Úweibull_max_gen._munpä  sG   € Ü�hŠh�s˜1˜S�5 �7•{Ó#ˆÜˆq‹6�A�:Œ:ØˆCð �yÐð ˆCØ�yÐr7   c                óx   € \         ) V,          \        P                  ! V4      ,
          \         ,           ^,           # r_   rA  r÷  s   &&r5   r  Úweibull_max_gen._entropyì  rC  r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r  r~   r„   r,  r  r‘   r’   r“   s   @r5   rˆ  rˆ  ©  s>   ø‡ € ñ#òHEò2ò:ò#òò&ò'ò÷4ð 4r7   rˆ  Úweibull_max)r™   rš   c                   ó`   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tRtV tR# )Úgenlogistic_genió  a1  A generalized logistic continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `genlogistic` is:

.. math::

    f(x, c) = c \frac{\exp(-x)}
                     {(1 + \exp(-x))^{c+1}}

for real :math:`x` and :math:`c > 0`. In literature, different
generalizations of the logistic distribution can be found. This is the type 1
generalized logistic distribution according to [1]_. It is also referred to
as the skew-logistic distribution [2]_.

`genlogistic` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

References
----------
.. [1] Johnson et al. "Continuous Univariate Distributions", Volume 2,
       Wiley. 1995.
.. [2] "Generalized Logistic Distribution", Wikipedia,
       https://en.wikipedia.org/wiki/Generalized_logistic_distribution

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úgenlogistic_gen._shape_info  r6  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r`  s   &&&r5   ru   Úgenlogistic_gen._pdf  r™  r7   c                ó&  € V^,
          ) V^ 8  ,          ^,
          p\         P                  ! V4      p\         P                  ! V4      W4,          ,           V^,           \        P                  ! \         P
                  ! V) 4      4      ,          ,
          # r_   )rQ   r	  r  r|   ré  rÓ   )rD   rt   r\  Úmultr  s   &&&  r5   rý   Úgenlogistic_gen._logpdf  s`   € ð �Q•ˆx˜1˜q™5Õ! AÕ%ˆÜ�vŠv�a‹yˆÜ�vŠv�a‹y˜4�9Õ$¨¨!­¬r¯xªx¼¿ºÀ¸u»Ó/FÕ'FÕFÐFr7   c                óR   € ^\         P                  ! V) 4      ,           V) ,          pV# r_   r7  )rD   rt   r\  ÚCxs   &&& r5   ry   Úgenlogistic_gen._cdf#  s!   € Ø”—’˜�r“
�l˜q˜bÕ!ˆØˆ	r7   c                óh   € V) \         P                  ! \         P                  ! V) 4      4      ,          # rO   )rQ   ré  rÓ   r`  s   &&&r5   r  Úgenlogistic_gen._logcdf'  s"   € Øˆr”B—H’HœRŸVšV Q B›ZÓ(Õ(Ð(r7   c                óh   € \         P                  ! \        P                  ! VRV,          4      4      ) # rš  )rQ   r  r|   Úpowm1rg  s   &&&r5   r„   Úgenlogistic_gen._ppf*  s#   € Ü—’”r—x’x  4¨¥6Ó*Ó+Ð+Ð+r7   c                óN   € \         P                  ! V P                  W4      4      ) # rO   ©r|   rf  r  r`  s   &&&r5   r~   Úgenlogistic_gen._sf-  ó   € Ü—’˜Ÿ™ aÓ+Ó,Ð,Ð,r7   c                ó4   € V P                  ^V,
          V4      # r_   ©r„   rg  s   &&&r5   rˆ   Úgenlogistic_gen._isf0  s   € Ø�y‰y˜˜Q� Ó"Ð"r7   c                ó  € \         \        P                  ! V4      ,           p\        P                  \        P                  ,          R ,          \        P
                  ! ^V4      ,           pR\        P
                  ! ^V4      ,          ^\        ,          ,           pV\        P                  ! VR4      ,          p\        P                  ^,          R,          ^\        P
                  ! ^V4      ,          ,           pWSR,          ,          pW#WE3# )rJ  rS  ç      .@rÒ   r<  )r#   r|   r•  rQ   r  Úzetar$   rU  ©rD   r\  ry  rz  r{  r|  s   &&    r5   r   Úgenlogistic_gen._stats3  s£   € Ü”b—f’f˜Q“iÕˆÜ�e‰e”B—E‘E�k˜#�o¤§¢¨¨1£Õ-ˆØ”—’˜˜1“Õ ¤&¥Õ(ˆØ
Œb�hŠh�s˜CÓ Õ ˆÜ�U‰U�A�X�d�]˜QœrŸwšw q¨!›}�_Õ,ˆØ
�3�h�ˆØ˜ˆÐr7   c                ó>   € \         P                  ! VR 8  VR R 4      # )g    €„^Ac                 ó˜   € \         P                  ! V 4      ) \        P                  ! V ^,           4      ,           \        ,           ^,           # r_   )rQ   r  r|   r•  r#   r–  s   &r5   r  Ú*genlogistic_gen._entropy.<locals>.<lambda>?  s)   € ”r—v’v˜a“y�j¤2§6¢6¨!¨a­%£=Õ0´6Õ9¸AÖ=r7   c                 óF   € ^^V ,          ,          \         ,           ^,           # r_   ©r#   r–  s   &r5   r  r½  E  s   € �a˜1˜q�5•k¤FÕ*¨QÖ.r7   r=  r÷  s   &&r5   r  Úgenlogistic_gen._entropy<  s$   € Ü�ŠØ�‰G�QÙ=ñ /ó0ð 	0r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r  r„   r~   rˆ   r   r  r‘   r’   r“   s   @r5   rŸ  rŸ  ó  sD   ø‡ € ñò@Eò*òGòò)ò,ò-ò#ò÷	0ð 	0r7   rŸ  Úgenlogisticc                   óv   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tRR ltR tR tRtV tR# )Úgenpareto_geniK  a=  A generalized Pareto continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `genpareto` is:

.. math::

    f(x, c) = (1 + c x)^{-1 - 1/c}

defined for :math:`x \ge 0` if :math:`c \ge 0`, and for
:math:`0 \le x \le -1/c` if :math:`c < 0`.

`genpareto` takes ``c`` as a shape parameter for :math:`c`.

For :math:`c=0`, `genpareto` reduces to the exponential
distribution, `expon`:

.. math::

    f(x, 0) = \exp(-x)

For :math:`c=-1`, `genpareto` is uniform on ``[0, 1]``:

.. math::

    f(x, -1) = 1

%(after_notes)s

%(example)s

c                ó.   € \         P                  ! V4      # rO   ©rQ   r$  r÷  s   &&r5   rd   Úgenpareto_gen._argchecko  ó   € Ü�{Š{˜1‹~Ðr7   c                ó^   € \        R R\        P                  ) \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úgenpareto_gen._shape_infor  ó%   € Ü˜3 ¬¯©¨´·±Ð'8¸.ÓIÐJÐJr7   c                óø   € \         P                  ! V4      p\         P                  ! V P                  V4      ^ ,          P	                  4       p\
        P                  ! V^ 8  VR \         P                  R7      pW#3# )r   c                 ó   € RV ,          # rš  r‹   r–  s   &r5   r  Ú,genpareto_gen._get_support.<locals>.<lambda>x  s   € °°a¶r7   r  )rQ   r#  rE  r˜   Úcopyr  r  rk   r\  s   &&  r5   r¥   Úgenpareto_gen._get_supportu  sZ   € Ü�JŠJ�q‹MˆÜ×Ò §¡¨Ó*¨1Õ-×2Ñ2Ó4ˆÜ�OŠO˜A ™E 1Ñ&7Ü')§v¡vô/ˆàˆtˆr7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r`  s   &&&r5   ru   Úgenpareto_gen._pdf|  r™  r7   c                óT   € \         P                  ! W8H  V^ 8g  ,          W3R V) R7      # )r   c                 óZ   € \         P                  ! VR ,           W,          4      ) V,          # r8  rÐ  ©rt   r\  s   &&r5   r  Ú'genpareto_gen._logpdf.<locals>.<lambda>‚  s   € ¬R¯ZªZ¸¸B½ÀÅÓ-DÐ,DÀqÖ,Hr7   r  r=  r`  s   &&&r5   rý   Úgenpareto_gen._logpdf€  s,   € Ü�Š ¡¨1°©6Õ2°Q°FÙHØ+,¨"ô.ð 	.r7   c                ó6   € \         P                  ! V) V) 4      ) # rO   )r|   Úinv_boxcox1pr`  s   &&&r5   ry   Úgenpareto_gen._cdf…  s   € Ü—’   Q BÓ'Ð'Ð'r7   c                ó4   € \         P                  ! V) V) 4      # rO   )r|   Ú
inv_boxcoxr`  s   &&&r5   r~   Úgenpareto_gen._sfˆ  s   € Ü�}Š}˜a˜R ! Ó$Ð$r7   c                óT   € \         P                  ! W8H  V^ 8g  ,          W3R V) R7      # )r   c                 óJ   € \         P                  ! W,          4      ) V,          # rO   r_  rÔ  s   &&r5   r  Ú&genpareto_gen._logsf.<locals>.<lambda>�  s   € ¬R¯XªX°aµc«]¨N¸QÖ,>r7   r  r=  r`  s   &&&r5   r
  Úgenpareto_gen._logsf‹  s,   € Ü�Š ¡¨1°©6Õ2°Q°FÙ>Ø+,¨"ô.ð 	.r7   c                ó6   € \         P                  ! V) V) 4      ) # rO   )r|   Úboxcox1prg  s   &&&r5   r„   Úgenpareto_gen._ppf�  s   € Ü—’˜Q˜B  Ó#Ð#Ð#r7   c                ó2   € \         P                  ! W) 4      ) # rO   )r|   Úboxcoxrg  s   &&&r5   rˆ   Úgenpareto_gen._isf“  s   € Ü—	’	˜!˜RÓ Ð Ð r7   c                ó¬  € R
w  r4rVRV9   d-   \         P                  ! V^8  VR \        P                  R7      pRV9   d-   \         P                  ! VR8  VR \        P                  R7      pRV9   d-   \         P                  ! VR8  VR \        P                  R7      pRV9   d-   \         P                  ! VR8  VR	 \        P                  R7      pW4WV3# )Nrì  c                 ó"   € ^^V ,
          ,          # r_   r‹   ©Úxis   &r5   r  Ú&genpareto_gen._stats.<locals>.<lambda>›  s   € ¨1°°Bµ®<r7   r  r  c                 óZ   € ^^V ,
          ^,          ,          ^^V ,          ,
          ,          # r_   r‹   ré  s   &r5   r  rë     s   € ¨1°°Bµ¸­{­?¸aÀ!ÀbÅ&½jÖ+Ir7   rj  c                 óž   € ^^V ,           ,          \         P                  ! ^^V ,          ,
          4      ,          ^^V ,          ,
          ,          # rD  rÇ  ré  s   &r5   r  rë  ¦  s/   € ˜1  B¥�<¬"¯'ª'°!°a¸µdµ(Ó*;Õ;¸qÀ1ÀRÅ4½xÖHr7   rk  c                 óØ   € ^^^V ,          ,
          ,          ^V ^,          ,          V ,           ^,           ,          ^^V ,          ,
          ,          ^^V ,          ,
          ,          ^,
          # r¥  r‹   ré  s   &r5   r  rë  ¬  sN   € ˜1  A b¥D¥�>¨Q¨r°1­u­W°r­\¸AÕ-=Õ>Ø ! B¥$�hõ(Ø+,¨q°­t­8õ5Ø78ö9r7   ©NNNNr£   gUUUUUUÕ?r¼  ©r  r  rQ   rk   rF  )rD   r\  rl  rì  r  rj  rk  s   &&&    r5   r   Úgenpareto_gen._stats–  s½   € Ø+‰
ˆˆaà�'Œ>Ü—’  A¡ qÙ 7Ü+-¯6©6ô3ˆAð �'Œ>Ü—’  C¡¨Ù IÜ+-¯6©6ô3ˆAð �'Œ>Ü—’Ø�C‘˜ÙHÜŸ6™6ô#ˆAð
 �'Œ>Ü—’Ø�C‘˜ñ9äŸ6™6ô	#ˆAð �QˆzÐr7   c           	     ó~   a€ V3R  lp\         P                  ! V^ 8g  W#\        P                  ! S^,           4      R7      # )c                 óv  <€ R p\         P                  ! ^ S^,           4      p\        V\        P                  ! SV4      4       F/  w  r4WRV,          ,          RW,          ,
          ,          ,           pK1  	  \         P
                  ! V S,          ^8  VRV ,          S,          ,          \         P                  4      # )r•   r–   r  r›  )rQ   r¯  Úzipr|   Úcombr±  rk   )r\  r˜  rk  ÚkiÚcnkrc   s   &    €r5   r¹  Ú#genpareto_gen._munp.<locals>.__munp³  s�   ø€ ØˆCÜ—	’	˜!˜Q �UÓ#ˆAÜ˜q¤"§'¢'¨!¨Q£-Ö0‘�Ø 2¨"¥*Õ,°°aµfµÕ=Õ=’ñ 1ä—8’8˜A �E A™I s¨d°Q­h¸1­_Õ'<¼b¿f¹fÓEÐEr7   r  )r  r  r|   r(  )rD   rc   r\  Ú_genpareto_gen__munps   &f& r5   r,  Úgenpareto_gen._munp²  s.   ø€ õ	Fô �Š˜q A™v q¼R¿XºXÀaÈ!Åe»_ÔMÐMr7   c                ó   € R V,           # r8  r‹   r÷  s   &&r5   r  Úgenpareto_gen._entropy¼  s   € Ø�A�vˆr7   r‹   Nrq  )rŒ   r�   rŽ   r�   r�   rd   rm   r¥   ru   rý   ry   r~   r
  r„   rˆ   r   r,  r  r‘   r’   r“   s   @r5   rÃ  rÃ  K  sS   ø‡ € ñ"òFòKòò*ò.ò
(ò%ò.ò
$ò!ôò8N÷ð r7   rÃ  Ú	genparetoc                   óN   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
tV tR# )Úgenexpon_geniÃ  aÕ  A generalized exponential continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `genexpon` is:

.. math::

    f(x, a, b, c) = (a + b (1 - \exp(-c x)))
                    \exp(-a x - b x + \frac{b}{c}  (1-\exp(-c x)))

for :math:`x \ge 0`, :math:`a, b, c > 0`.

`genexpon` takes :math:`a`, :math:`b` and :math:`c` as shape parameters.

%(after_notes)s

References
----------
H.K. Ryu, "An Extension of Marshall and Olkin's Bivariate Exponential
Distribution", Journal of the American Statistical Association, 1993.

N. Balakrishnan, Asit P. Basu (editors), *The Exponential Distribution:
Theory, Methods and Applications*, Gordon and Breach, 1995.
ISBN 10: 2884491929

%(example)s

c                ó¾   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      p\        RR^ \        P                  3R4      pWV.# )r˜   Fr™   r\  r4  rj   )rD   r£  r¤  ry  s   &   r5   rm   Úgenexpon_gen._shape_infoã  sT   € Ü˜˜U Q¬¯© K°Ó@ˆÜ˜˜U Q¬¯© K°Ó@ˆÜ˜˜U Q¬¯© K°Ó@ˆØ˜ˆ|Ðr7   c           	     ó  € W#\         P                  ! V) V,          4      ) ,          ,           \        P                  ! V) V,
          V,          V\         P                  ! V) V,          4      ) ,          V,          ,           4      ,          # rO   ©r|   rf  rQ   rÓ   ©rD   rt   r˜   r™   r\  s   &&&&&r5   ru   Úgenexpon_gen._pdfé  sf   € ð œŸš !  A¥›�Õ'Õ'¬¯ª°!°°Aµ°qµØ01´B·H²H¸a¸RÀ½T³N°?Õ0CÀAÕ0Eõ1Fó *Gõ Gð 	Gr7   c                ó  € \         P                  ! W#\        P                  ! V) V,          4      ) ,          ,           4      V) V,
          V,          ,           V\        P                  ! V) V,          4      ) ,          V,          ,           # rO   ©rQ   r  r|   rf  r  s   &&&&&r5   rý   Úgenexpon_gen._logpdfï  sW   € Ü�vŠv�aœBŸHšH a R¨¥T›N˜?Õ+Õ+Ó,°°°1µ°a­xÕ7¸¼B¿HºHÀaÀRÈÅT»N¸?Õ8KÈAÕ8MÕMÐMr7   c                ó²   € \         P                  ! V) V,
          V,          V\         P                  ! V) V,          4      ) ,          V,          ,           4      ) # rO   r=  r  s   &&&&&r5   ry   Úgenexpon_gen._cdfò  s=   € Ü—’˜1˜"˜Q�$ � A¬¯ª°!°°Aµ« Õ$7¸Õ$9Õ9Ó:Ð:Ð:r7   c                ó  € W#,           pW4\         P                  ! V) 4      ,          ,
          V,          pV\        P                  ! V) V,          \         P                  ! V) 4      ,          4      P
                  ,           V,          # rO   )rQ   ré  r|   ÚlambertwrÓ   Úreal©rD   rH  r˜   r™   r\  rj  r±  s   &&&&&  r5   r„   Úgenexpon_gen._ppfõ  sX   € Ø�EˆØ”2—8’8˜Q˜B“<•Õ Õ"ˆØ”B—K’K   1¥¤r§v¢v¨q¨b£zÕ 1Ó2×7Ñ7Õ7¸Õ:Ð:r7   c                ó°   € \         P                  ! V) V,
          V,          V\        P                  ! V) V,          4      ) ,          V,          ,           4      # rO   r¡  r  s   &&&&&r5   r~   Úgenexpon_gen._sfú  s:   € Ü�vŠv˜�r˜!•t˜Q•h ¤R§X¢X¨q¨b°­d£^ OÕ!4°QÕ!6Õ6Ó7Ð7r7   c                ó
  € W#,           pW4\         P                  ! V4      ,          ,
          V,          pV\        P                  ! V) V,          \         P                  ! V) 4      ,          4      P
                  ,           V,          # rO   )rQ   r  r|   r  rÓ   r  r  s   &&&&&  r5   rˆ   Úgenexpon_gen._isfý  sU   € Ø�EˆØ”2—6’6˜!“9•�_˜aÕˆØ”B—K’K   1¥¤r§v¢v¨q¨b£zÕ 1Ó2×7Ñ7Õ7¸Õ:Ð:r7   r‹   Nr�  r“   s   @r5   rÿ  rÿ  Ã  s4   ø‡ € ñò>òGòNò;ò;ò
8÷;ð ;r7   rÿ  Úgenexponc                   óŠ   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tV 3R ltR tR tRtVtV ;t# )Úgenextreme_geni  aê  A generalized extreme value continuous random variable.

%(before_notes)s

See Also
--------
gumbel_r

Notes
-----
For :math:`c=0`, `genextreme` is equal to `gumbel_r` with
probability density function

.. math::

    f(x) = \exp(-\exp(-x)) \exp(-x),

where :math:`-\infty < x < \infty`.

For :math:`c \ne 0`, the probability density function for `genextreme` is:

.. math::

    f(x, c) = \exp(-(1-c x)^{1/c}) (1-c x)^{1/c-1},

where :math:`-\infty < x \le 1/c` if :math:`c > 0` and
:math:`1/c \le x < \infty` if :math:`c < 0`.

Note that several sources and software packages use the opposite
convention for the sign of the shape parameter :math:`c`.

`genextreme` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó.   € \         P                  ! V4      # rO   rÅ  r÷  s   &&r5   rd   Úgenextreme_gen._argcheck-  rÇ  r7   c                ó^   € \        R R\        P                  ) \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úgenextreme_gen._shape_info0  rÊ  r7   c                ó0  € \         P                  ! V^ 8„  R\         P                  ! V\        4      ,          \         P                  4      p\         P                  ! V^ 8  R\         P
                  ! V\        ) 4      ,          \         P                  ) 4      pW23# ©r   r–   )rQ   r±  Úmaximumr!   rk   Úminimum)rD   r\  Ú_bÚ_as   &&  r5   r¥   Úgenextreme_gen._get_support3  sa   € Ü�XŠX�a˜!‘e˜S¤2§:¢:¨a´Ó#7Õ7¼¿¹Ó@ˆÜ�XŠX�a˜!‘e˜S¤2§:¢:¨a´%°Ó#8Õ8¼2¿6¹6¸'ÓBˆØˆvˆr7   c                óT   € \         P                  ! W8H  V^ 8g  ,          W3R V) R7      # )r   c                 óL   € \         P                  ! V) V ,          4      V,          # rO   r_  rÔ  s   &&r5   r  Ú+genextreme_gen._loglogcdf.<locals>.<lambda><  s   € œŸš 1 " Q¥$›¨Ö)r7   r  r=  r`  s   &&&r5   Ú
_loglogcdfÚgenextreme_gen._loglogcdf8  s-   € ä�ŠØ‰V˜˜Q™Õ ! Ù)Ø�rôð 	r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r`  s   &&&r5   ru   Úgenextreme_gen._pdf?  s   € ô �vŠv�d—l‘l 1Ó(Ó)Ð)r7   c                ó,  € \         P                  ! W8H  V^ 8g  ,          W!3\        P                  RR7      p\        P
                  ! V) 4      pV P                  W4      p\        P                  ! V4      p\        P                  ! WR^ 8H  V\        P                  ) 8H  ,          R4       \         P                  ! V^8H  V\        P                  ) 8H  ,          ( WeV3R \        P                  ) R7      p\        P                  ! Wr^8H  V^8H  ,          R4       V# )r   r•   r  c                 ó$   € V ) V,           V,
          # rO   r‹   )Úpex2Úlpex2Úlex2s   &&&r5   r  Ú(genextreme_gen._logpdf.<locals>.<lambda>Q  s   €  t e¨e¥m°dÖ&:r7   )r  r  ÚoperatorÚmulr|   ré  r%  rQ   rÓ   Úputmaskrk   )rD   rt   r\  ÚcxÚlogex2Úlogpex2r+  Úlogpdfs   &&&     r5   rý   Úgenextreme_gen._logpdfE  sÒ   € ä�_Š_˜a™f¨¨a©Õ0°1°&Ü%Ÿ\™\°cô;ˆä—’˜2˜#“ˆØ—/‘/ !Ó'ˆÜ�vŠv�g‹ˆä
�
Š
�7 !™V¨¬b¯f©f¨W©Õ5°sÔ;Ü—’Ø�Q‰w˜2¤"§&¡& ™=Õ)Ð*Ø˜FÐ#Ù:ÜŸ™�wô	 ˆô
 	�
Š
�6 ™F q¨A¡vÕ.°Ô4Øˆr7   c                óN   € \         P                  ! V P                  W4      4      ) # rO   )rQ   rÓ   r%  r`  s   &&&r5   r  Úgenextreme_gen._logcdfV  s   € Ü—’�t—‘ qÓ,Ó-Ð-Ð-r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r  r`  s   &&&r5   ry   Úgenextreme_gen._cdfY  r`  r7   c                óN   € \         P                  ! V P                  W4      4      ) # rO   r°  r`  s   &&&r5   r~   Úgenextreme_gen._sf\  r²  r7   c                óª   € \         P                  ! \         P                  ! V4      ) 4      ) p\        P                  ! W38H  V^ 8g  ,          W23R VR7      # )r   c                 óN   € \         P                  ! V) V ,          4      ) V,          # rO   r=  rÔ  s   &&r5   r  Ú%genextreme_gen._ppf.<locals>.<lambda>c  ó   € œ"Ÿ(š( A 2¨¥6Ó*Ð*¨QÖ.r7   r  )rQ   r  r  r  ©rD   rƒ   r\  rt   s   &&& r5   r„   Úgenextreme_gen._ppf_  sF   € Ü�VŠV”R—V’V˜A“Y�JÓÐˆÜ�ŠØ‰V˜˜Q™Õ ! Ù.Øôð 	r7   c                ó¬   € \         P                  ! \        P                  ! V) 4      ) 4      ) p\        P
                  ! W38H  V^ 8g  ,          W23R VR7      # )r   c                 óN   € \         P                  ! V) V ,          4      ) V,          # rO   r=  rÔ  s   &&r5   r  Ú%genextreme_gen._isf.<locals>.<lambda>j  r@  r7   r  )rQ   r  r|   ré  r  r  rA  s   &&& r5   rˆ   Úgenextreme_gen._isff  sH   € Ü�VŠV”R—X’X˜q˜b“\�MÓ"Ð"ˆÜ�ŠØ‰V˜˜Q™Õ ! Ù.Øôð 	r7   c                ó  a€ V3R  lpV! ^4      pV! ^4      pV! ^4      pV! ^4      p\         P                  ! \        S4      R8  S\         P                  ,          R,          R,          WCR,          ,
          4      pR p\        P
                  ! \        S4      R8¬  SV\         P                  R,          R,          R7      p	Rp
R p\        P
                  ! \        S4      V
8¬  SV\        ) R7      p\         P                  ! SR8  \         P                  V) 4      p\         P                  ! SR8  \         P                  VR,          V	,          4      pR p^\         P                  ! ^4      ,          \        ,          \         P                  ^,          ,          pW4WW3p\        P
                  ! \        S4      V
R	,          8„  S.VO5VVR7      pR
 pW4WVV3p\        P
                  ! \        S4      V
R,          8„  S.VO5VRR7      pWÞVV3# )c                 óL   <€ \         P                  ! V S,          ^,           4      # r_   r'  )rc   r\  s   &€r5   ÚgÚ genextreme_gen._stats.<locals>.gn  s   ø€ Ü—8’8˜A �E A�IÓ&Ð&r7   gH¯¼šò×z>rÒ   rJ  c                 óà   € \         P                  ! \         P                  ! R V ,          R,           4      ^\         P                  ! V R,           4      ,          ,
          4      V R ,          ,          # r  ©r|   rf  r  r–  s   &r5   Úgam2k_fÚ&genextreme_gen._stats.<locals>.gam2k_fu  sB   € Ü—8’8œBŸJšJ s¨1¥u¨S¥yÓ1°!´B·J²J¸qÀ3½wÓ4GÕ2GÕGÓHÈÈCÍÕOÐOr7   r  ç›+¡†›„=c                 ór   € \         P                  ! \         P                  ! V ^,           4      4      V ,          # r_   rL  r–  s   &r5   Úgamk_fÚ%genextreme_gen._stats.<locals>.gamk_fy  s#   € Ü—8’8œBŸJšJ q¨1¥uÓ-Ó.¨qÕ0Ð0r7   c                 óf   € R  p\         P                  ! V R8¬  V .VO5V\        P                  R7      # )c                 ó’   € \         P                  ! V 4      V) V^V,          ,           V,          ,           ,          VR,          ,          # ©rÑ   rS  rP   )r\  r{  r|  Úg3Úg2mg12s   &&&&&r5   Ú
sk1_eval_fÚ;genextreme_gen._stats.<locals>.sk1_eval.<locals>.sk1_eval_f…  s2   € Ü—w’w˜q“z B 3¨"¨q°­x­-¸Õ);Õ#;Õ<¸VÀS½[ÕHÐHr7   r  rˆ  rÛ  )r\  rF   rX  s   &* r5   Úsk1_evalÚ'genextreme_gen._stats.<locals>.sk1_eval„  s2   € òIä—?’? 1¨¡:°¨z°D©zØ#-¼"¿&¹&ôBð Br7   g�Âõ(\�Ò?c                 ó\   € R  p\         P                  ! V R8¬  W\        P                  R7      # )c                 ó�   € VRV,          ^W,           ,          V ,          ,           V ,          ,           V^,          ,          ^,
          # )rU  r`  r‹   )r{  r|  rV  Úg4rW  s   &&&&&r5   Ú
ku1_eval_fÚ;genextreme_gen._stats.<locals>.ku1_eval.<locals>.ku1_eval_f‘  s4   € Ø˜b �e a¨­¥o°bÕ&8Õ8¸"Õ<Õ<¸fÀa½iÕGÈ!ÕKÐKr7   r  g      Ð¿rÛ  )r\  rF   r_  s   &* r5   Úku1_evalÚ'genextreme_gen._stats.<locals>.ku1_eval�  s#   € òLä—?’? 1¨¡:¨tÌBÏFÉFÔSÐSr7   gq=
×£pÍ?r›  r#  ç333333@)
rQ   r±  r	  r  r  r  r#   rF  r'  r$   )rD   r\  rI  r{  r|  rV  r^  rW  rM  Úgam2kÚepsrQ  Úgamkrì  r  rZ  Úsk_fillrF   rÒ  ra  rÓ  s   &f                   r5   r   Úgenextreme_gen._statsm  s¡  ø€ õ	'áˆq‹TˆÙˆq‹TˆÙˆq‹TˆÙˆq‹TˆÜ—’œ#˜a›& 4™-¨!¬B¯E©E­'°C­¸Õ);¸RÀCÅ½ZÓHˆò	Pä—’¤ A£¨$¡°°7ÄrÇuÁuÈcÅzÐRUÅ~ÔVˆØˆò	1ä�Šœs 1›v¨™}¨a°ÄVÀGÔLˆô �HŠH�Q˜‘XœrŸv™v¨ uÓ-ˆô �HŠH�Q˜‘XœrŸv™v r¨3¥w¨u¥}Ó5ˆò	Bð ”R—W’W˜Q“Z•-¤Õ&¤r§u¡u¨a¥xÕ/ˆØ˜Ð#ˆÜ�_Š_œS ›V c¨4¥iÑ/°!°°d±Ø%°'ô;ˆò	Tð
 ˜ Ð'ˆÜ�_Š_œS ›V c¨4¥iÑ/°!°°d±Ø%°(ô<ˆð �R˜ˆ|Ðr7   c                ó    <€ \        V\        4      '       d   VP                  4       p\        V4      pV^ 8  d   RpMRp\        SV `  W3R7      # )r   r£   r…  r#  ©r>   r)   rÕ  r   r@   r×  )rD   rE   rI  r˜   rØ  s   &&  €r5   r×  Úgenextreme_gen._fitstart›  sK   ø€ Ü�dœL×)Ò)Ø—>‘>Ó#ˆDä�$‹KˆØˆqŒ5Ø‰AàˆAÜ‰wÑ  ¨DÐ Ó1Ð1r7   c                óˆ  € \         P                  ! ^ V^,           4      pRW!,          ,          \         P                  ! \        P                  ! W4      RV,          ,          \        P
                  ! W#,          ^,           4      ,          ^ R7      ,          p\         P                  ! W!,          R8„  V\         P                  4      # )r   r–   rO  r  )rQ   r¯  rè  r|   rõ  r(  r±  rk   )rD   rc   r\  rk  Úvalss   &&&  r5   r,  Úgenextreme_gen._munp¦  s{   € Ü�IŠI�a˜˜1�ÓˆØ�1•4�xœ"Ÿ&š&Ü�GŠG�A‹M˜R !�GÕ#¤b§h¢h¨q­s°Q­wÓ&7Õ7Øôõ ˆô �xŠx˜�˜b™ $¬¯©Ó/Ð/r7   c                ó8   € \         ^V,
          ,          ^,           # r_   r¿  r÷  s   &&r5   r  Úgenextreme_gen._entropy­  s   € Ü�q˜1•u�~ Õ!Ð!r7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   r¥   r%  ru   rý   r  ry   r~   r„   rˆ   r   r×  r,  r  r‘   r’   r  r   s   @@r5   r  r    s]   ù‡ € ñ%òLòKòò
ò*òò".ò*ò-òòò,õ\	2ò0÷"ò "r7   r  Ú
genextremec                ó�  a € RpV 3R lpS R8”  d@   \         P                  ! S 4      R,           pS ^
8  d   \        P                  ! W#RR7      pV# M=S R8”  d&   \         P                  ! S R,          4      R,           pMRS ) V,
          ,          p\        P                  ! W#R	R
R7      w  rErgV^8w  d   \        RS : 24      hV^ ,          # )a2  Inverse of the digamma function (real positive arguments only).

This function is used in the `fit` method of `gamma_gen`.
The function uses either optimize.fsolve or optimize.newton
to solve `sc.digamma(x) - y = 0`.  There is probably room for
improvement, but currently it works over a wide range of y:

>>> import numpy as np
>>> rng = np.random.default_rng()
>>> y = 64*rng.standard_normal(1000000)
>>> y.min(), y.max()
(-311.43592651416662, 351.77388222276869)
>>> x = [_digammainv(t) for t in y]
>>> np.abs(sc.digamma(x) - y).max()
1.1368683772161603e-13

g¶oüŒxâ?c                 ó>   <€ \         P                  ! V 4      S,
          # rO   )r|   rZ  ru  s   &€r5   r˜  Ú_digammainv.<locals>.funcÈ  s   ø€ Ü�zŠz˜!‹}˜qÕ Ð r7   r£   ç»½×Ùß|Û=)Útolg-²�ï§@gë­�­,¶?r–   ç•dyáý¥=T)ÚxtolrÜ  z _digammainv: fsolve failed, y = g      À¿r_  )rQ   rÓ   r   ÚnewtonrÖ  ÚRuntimeError)rv  Ú_emr˜  Úx0Úvaluerì  rí  r�  s   f       r5   Ú_digammainvr~  ´  s¸   ø€ ð$ &€Cõ!ð 	ˆ6„zÜ�VŠV�A‹Y˜�_ˆØˆrŒ6ô —O’O D°%Ô8ˆEØˆLð ð 
ˆRŒÜ�VŠV�A�e•G‹_˜wÕ&‰à�Q�B˜•HÕˆä%Ÿ_š_¨T¸EØ9=ô?Ñ€E�à
ˆa„xÜÐ=¸a¹UÐCÓDÐDà��8€Or7   c                   ó¢   a a€ ] tR tRt oRtR tRR ltR tR tR t	R t
R	 tR
 tR tR tR tV 3R lt]! ]RR7      V 3R l4       tRtVtV ;t# )Ú	gamma_geniæ  a3  A gamma continuous random variable.

%(before_notes)s

See Also
--------
erlang, expon

Notes
-----
The probability density function for `gamma` is:

.. math::

    f(x, a) = \frac{x^{a-1} e^{-x}}{\Gamma(a)}

for :math:`x \ge 0`, :math:`a > 0`. Here :math:`\Gamma(a)` refers to the
gamma function.

`gamma` takes ``a`` as a shape parameter for :math:`a`.

When :math:`a` is an integer, `gamma` reduces to the Erlang
distribution, and when :math:`a=1` to the exponential distribution.

Gamma distributions are sometimes parameterized with two variables,
with a probability density function of:

.. math::

    f(x, \alpha, \beta) =
    \frac{\beta^\alpha x^{\alpha - 1} e^{-\beta x }}{\Gamma(\alpha)}

Note that this parameterization is equivalent to the above, with
``scale = 1 / beta``.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r3  rj   rl   s   &r5   rm   Úgamma_gen._shape_info  r6  r7   c                ó$   € VP                  W4      # rO   ©Ústandard_gamma)rD   r˜   rô   rõ   s   &&&&r5   rö   Úgamma_gen._rvs  s   € Ø×*Ñ*¨1Ó3Ð3r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r9  s   &&&r5   ru   Úgamma_gen._pdf  r™  r7   c                ó‚   € \         P                  ! VR ,
          V4      V,
          \         P                  ! V4      ,
          # r8  )r|   rµ  r  r9  s   &&&r5   rý   Úgamma_gen._logpdf  s)   € Ü�xŠx˜˜#�˜qÓ! AÕ%¬¯
ª
°1«Õ5Ð5r7   c                ó.   € \         P                  ! W!4      # rO   rA  r9  s   &&&r5   ry   Úgamma_gen._cdf  rŠ   r7   c                ó.   € \         P                  ! W!4      # rO   rE  r9  s   &&&r5   r~   Úgamma_gen._sf  s   € Ü�|Š|˜AÓ!Ð!r7   c                ó.   € \         P                  ! W!4      # rO   r~  rA  s   &&&r5   r„   Úgamma_gen._ppf"  s   € Ü�~Š~˜aÓ#Ð#r7   c                ó.   € \         P                  ! W!4      # rO   ©r|   rP  rA  s   &&&r5   rˆ   Úgamma_gen._isf%  s   € Ü�Š˜qÓ$Ð$r7   c                óP   € WR \         P                  ! V4      ,          RV,          3# )rÒ   rJ  rÇ  rG  s   &&r5   r   Úgamma_gen._stats(  s   € Ø�SœŸš ›•^ S¨¥UÐ*Ð*r7   c                ó.   € \         P                  ! W!4      # rO   ©r|   rT  ©rD   rc   r˜   s   &&&r5   r,  Úgamma_gen._munp+  s   € Ü�wŠw�q‹}Ðr7   c                óD   € R  pR p\         P                  ! V^ú8  WV4      # )c                 óŽ   € \         P                  ! V 4      ^V ,
          ,          V ,           \         P                  ! V 4      ,           # r_   ©r|   r•  r  ©r˜   s   &r5   r\  Ú+gamma_gen._entropy.<locals>.regular_formula0  s+   € Ü—6’6˜!“9  !¥Õ$ qÕ(¬2¯:ª:°a«=Õ8Ð8r7   c                 óR  € R R\         P                  ! ^\         P                  ,          4      ,           \         P                  ! V 4      ,           ,          ^^V ,          ,          ,
          V R,          ^,          ,
          V R,          ^Z,          ,
          V R,          ^x,          ,           # )r£   r–   rö  r÷  rø  r  r�  s   &r5   ra  Ú.gamma_gen._entropy.<locals>.asymptotic_formula3  sq   € ð
 ˜2¤§¢ q¬¯©¥w£Õ/´"·&²&¸³)Õ;Õ<¸qÀ!ÀaÅ%½yÕHØ˜#•v˜r•kõ"Ø%&¨¥V¨R¥Kõ0Ø34°cµ6¸3µ,õ?ð @r7   r=  )rD   r˜   r\  ra  s   &&  r5   r  Úgamma_gen._entropy.  s'   € ò	9ò	@ô �Š˜q 3™w¨Ð<NÓOÐOr7   c                ó¶   <€ \        V\        4      '       d   VP                  4       p\        V4      p^RV^,          ,           ,          p\        SV `  W3R7      # )rU  ç:Œ0âŽyE>r…  rj  )rD   rE   rÒ  r˜   rØ  s   &&  €r5   r×  Úgamma_gen._fitstart=  sN   ø€ ô �dœL×)Ò)Ø—>‘>Ó#ˆDÜ�4‹[ˆØ�˜˜A�•ÕˆÜ‰wÑ  ¨DÐ Ó1Ð1r7   a<          When the location is fixed by using the argument `floc`
        and `method='MLE'`, this
        function uses explicit formulas or solves a simpler numerical
        problem than the full ML optimization problem.  So in that case,
        the `optimizer`, `loc` and `scale` arguments are ignored.
        

r  c                ó,  <a€ VP                  R R4      pVP                  RR4      p\        V\        4      '       g   Vf*   VP                  4       R8w  d   \        SV `  ! V.VO5/ VB # VP                  R R4       \        V. RO4      pVP                  RR4      p\        V4       Ve   Ve   Ve   \        R4      h\        P                  ! V4      p\        P                  ! V4      P                  4       '       g   \        R4      hVP                  4       R8X  dÿ   \        P                  ! V4      p\        P                  ! V4      p	\        P                  ! W,
          ^,          4      p
YdTrÜpVf   Vf   Vf   V
^V	,          ,          pVf!   Vf   \        P                   ! W›,          4      pVf   Vf   W˜V,
          ,          pVf   Vf   W�^,          ,          pVf   WŒ,
          V,          pVf   W‹V,          ,
          pVf   WŒ,
          V,          pW¼V3# \        P"                  ! W8*  4      '       d   \%        RV\        P&                  R	7      hV^ 8w  d	   W,
          pVP                  4       pVfÎ   Ve   TpM½\        P(                  ! V4      \        P(                  ! V4      P                  4       ,
          o^S,
          \        P                   ! S^,
          ^,          ^S,          ,           4      ,           ^S,          ,          pVR,          pVR,          p\*        P,                  ! V3R
 lVV^ R7      pWë,          pML\        P(                  ! V4      P                  4       \        P(                  ! V4      ,
          p\/        V4      pTpW´V3# )r  Nr0   r:   r;   r  r   r!  r(  rÛ  c                 ót   <€ \         P                  ! V 4      \        P                  ! V 4      ,
          S,
          # rO   )rQ   r  r|   rZ  )r˜   rj  s   &€r5   r  Úgamma_gen.fit.<locals>.<lambda>§  s   ø€ ¬b¯fªf°Q«i¼"¿*º*ÀQ»-Õ.GÈ!Ö.Kr7   )ÚdisprÞ  g333333ã?gffffffö?)r<   r>   r)   r=   r@   rB   r2   r   r6   r"  rQ   r#  r$  r%  r&  rê  r'  ræ  rƒ  rk   r  r   Úbrentqr~  )rD   rE   rF   r4   r  r0   rß  r  Úm1Úm2Úm3r˜   r-   r.   rë  ÚaestÚxar›  r\  rj  rØ  s   &&*,               @€r5   rB   Úgamma_gen.fitI  sà  ù€ ð �x‰x˜ Ó%ˆØ—‘˜( EÓ*ˆä�tœ\×*Ò*Ø’ §¡£°4Ô!7ô ‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ð 	�‰�˜Ôä! $Ò(=Ó>ˆØ—‘˜( DÓ)ˆä$ TÔ*àŠ>˜dÒ.°6Ò3Eô ð )ó *ð *ô �zŠz˜$Óˆä�{Š{˜4Ó ×$Ñ$×&Ò&ÜÐCÓDÐDð �<‰<‹>˜TÔ!Ü—’˜“ˆBÜ—’˜“ˆBÜ—’˜$�)¨Õ)Ó*ˆBØ f�EˆAàŠy˜Sš[¨Uª]Ø˜a "�f��àŠ{˜uš}ÜŸš ¥›�ØŠy˜Uš]Ø 3�h��ØŠy˜Sš[Ø 1�*Õ%�àŠyØ•X Õ&�ØŠ{Ø˜u�9•n�ØŠ}Ø� Q��Ø˜5�=Ð ô
 �6Š6�$‘,×ÒÜ˜w¨d¼"¿&¹&ÔAÐAà�1Œ9ð •;ˆDØ�y‰y‹{ˆð Š>àŠ~à‘ô —F’F˜4“L¤2§6¢6¨$£<×#4Ñ#4Ó#6Õ6�Ø˜!�œbŸgšg q¨¥s¨Q¥h°°Aµ¥oÓ6Õ6¸2¸a½4Õ@�Ø˜5•\�Ø˜5•\�Ü—O’OÔ$KØ$&¨°ô4�ð
 •H‰Eô
 —’�t“×!Ñ!Ó#¤b§f¢f¨V£nÕ4ˆAÜ˜A“ˆAØˆEà˜ˆ~Ðr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r~   r„   rˆ   r   r,  r  r×  r	   r   rB   r‘   r’   r  r   s   @@r5   r€  r€  æ  sq   ù‡ € ñ'òPEô4ò*ò6ò!ò"ò$ò%ò+òòPõ
2ñ ˜}ð 5ô ôeó÷eð er7   r€  r(  c                   óh   a a€ ] tR tRt oRtR tR tV 3R lt]! ]	RR7      V 3R l4       t
R	tVtV ;t# )
Ú
erlang_geni»  a�  An Erlang continuous random variable.

%(before_notes)s

See Also
--------
gamma

Notes
-----
The Erlang distribution is a special case of the Gamma distribution, with
the shape parameter `a` an integer.  Note that this restriction is not
enforced by `erlang`. It will, however, generate a warning the first time
a non-integer value is used for the shape parameter.

Refer to `gamma` for examples.

c                ó¾   € \         P                  ! \         P                  ! V4      V8H  4      pV'       g%   R V: R2p\        P                  ! V\
        ^R7       V^ 8„  # )zRThe shape parameter of the erlang distribution has been given a non-integer value r1   ©Ú
stacklevel)rQ   r%  r  ÚwarningsÚwarnÚRuntimeWarning)rD   r˜   ÚallintÚmessages   &&  r5   rd   Úerlang_gen._argcheckÏ  sM   € Ü—’œŸš › qÑ(Ó)ˆßð=Ø=>¹EÀðDˆGä�MŠM˜'¤>¸aÕ@Ø�1‰uˆr7   c                ó@   € \        R R^\        P                  3R4      .# )r˜   Tri   rj   rl   s   &r5   rm   Úerlang_gen._shape_infoÙ  ro   r7   c                óÌ   <€ \        V\        4      '       d   VP                  4       p\        R R\	        V4      ^,          ,           ,          4      p\
        \        V `  W3R7      # )r¬  r£  r…  )r>   r)   rÕ  r+  r   r@   r€  r×  )rD   rE   r˜   rØ  s   && €r5   r×  Úerlang_gen._fitstartÜ  sQ   ø€ ô �dœL×)Ò)Ø—>‘>Ó#ˆDÜ��tœe D›k¨1�nÕ,Õ-Ó.ˆÜ”Y Ñ/°¸4Ð/Ó@Ð@r7   a¦          The Erlang distribution is generally defined to have integer values
        for the shape parameter.  This is not enforced by the `erlang` class.
        When fitting the distribution, it will generally return a non-integer
        value for the shape parameter.  By using the keyword argument
        `f0=<integer>`, the fit method can be constrained to fit the data to
        a specific integer shape parameter.r  c                ó,   <€ \         SV `  ! V.VO5/ VB # rO   )r@   rB   ©rD   rE   rF   r4   rØ  s   &&*,€r5   rB   Úerlang_gen.fitç  s   ø€ ô ‰wŠ{˜4Ð/ $Ò/¨$Ñ/Ð/r7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   r×  r	   r   rB   r‘   r’   r  r   s   @@r5   r±  r±  »  s@   ù‡ € ñò&òCõAñ ˜}ð 5/ô 0ô0ó0÷0ð 0r7   r±  Úerlangc                   ój   a € ] tR tRt o RtR tR tR tR tR t	RR	 lt
R
 tR tR tR tR tRtV tR# )Úgengamma_geniõ  aq  A generalized gamma continuous random variable.

%(before_notes)s

See Also
--------
gamma, invgamma, weibull_min

Notes
-----
The probability density function for `gengamma` is ([1]_):

.. math::

    f(x, a, c) = \frac{|c| x^{c a-1} \exp(-x^c)}{\Gamma(a)}

for :math:`x \ge 0`, :math:`a > 0`, and :math:`c \ne 0`.
:math:`\Gamma` is the gamma function (`scipy.special.gamma`).

`gengamma` takes :math:`a` and :math:`c` as shape parameters.

%(after_notes)s

References
----------
.. [1] E.W. Stacy, "A Generalization of the Gamma Distribution",
   Annals of Mathematical Statistics, Vol 33(3), pp. 1187--1192.

%(example)s

c                ó    € V^ 8„  V^ 8g  ,          # r  r‹   )rD   r˜   r\  s   &&&r5   rd   Úgengamma_gen._argcheck  s   € Ø�A‘˜!˜q™&Õ!Ð!r7   c                óž   € \        R R^ \        P                  3R4      p\        RR\        P                  ) \        P                  3R4      pW.# r{  rj   r|  s   &  r5   rm   Úgengamma_gen._shape_info  ó@   € Ü˜˜U Q¬¯© K°Ó@ˆÜ˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆØˆxˆr7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  r  s   &&&&r5   ru   Úgengamma_gen._pdf  ó   € Ü�vŠv�d—l‘l 1¨Ó+Ó,Ð,r7   c                ót   € \         P                  ! V^ 8g  V^ 8„  ,          WV3R \        P                  ) R7      # )r   c                 óâ   € \         P                  ! \        V4      4      \        P                  ! W,          ^,
          V 4      ,           W,          ,
          \        P
                  ! V4      ,
          # r_   )rQ   r  r	  r|   rµ  r  )rt   r\  r˜   s   &&&r5   r  Ú&gengamma_gen._logpdf.<locals>.<lambda>#  s@   € œRŸVšV¤C¨£F›^¬b¯hªh°qµs¸QµwÀÓ.BÕBØ �tõ$Ü&(§j¢j°£mö4r7   r  rU  r  s   &&&&r5   rý   Úgengamma_gen._logpdf   s7   € Ü�ŠØ�!‰V˜˜A™Õ  q 	ñ5äŸ™�wô	 ð 	 r7   c                óž   € W,          p\         P                  ! W$4      p\         P                  ! W$4      p\        P                  ! V^ 8„  WV4      # r  ©r|   rB  rF  rQ   r±  ©rD   rt   r˜   r\  ÚxcÚval1Úval2s   &&&&   r5   ry   Úgengamma_gen._cdf'  ó:   € Ø�TˆÜ�{Š{˜1Ó!ˆÜ�|Š|˜AÓ"ˆÜ�xŠx˜˜A™˜tÓ*Ð*r7   Nc                óF   € VP                  WR 7      pVRV,          ,          # )r³  r–   r„  )rD   r˜   r\  rô   rõ   rI  s   &&&&& r5   rö   Úgengamma_gen._rvs-  s#   € Ø×'Ñ'¨Ð'Ó5ˆØ�2�a•4�yÐr7   c                óž   € W,          p\         P                  ! W$4      p\         P                  ! W$4      p\        P                  ! V^ 8„  We4      # r  rÒ  rÓ  s   &&&&   r5   r~   Úgengamma_gen._sf1  rØ  r7   c                óª   € \         P                  ! W!4      p\         P                  ! W!4      p\        P                  ! V^ 8„  WE4      RV,          ,          # r  ©r|   rK  rP  rQ   r±  ©rD   rƒ   r˜   r\  rÕ  rÖ  s   &&&&  r5   r„   Úgengamma_gen._ppf7  ó<   € Ü�~Š~˜aÓ#ˆÜ�Š˜qÓ$ˆÜ�xŠx˜˜A™˜tÓ*¨S°­UÕ3Ð3r7   c                óª   € \         P                  ! W!4      p\         P                  ! W!4      p\        P                  ! V^ 8„  WT4      RV,          ,          # r  rÞ  rß  s   &&&&  r5   rˆ   Úgengamma_gen._isf<  rá  r7   c                óJ   € \         P                  ! W!R ,          V,          4      # r8  r—  )rD   rc   r˜   r\  s   &&&&r5   r,  Úgengamma_gen._munpA  s   € ä�wŠw�q˜C�% �'Ó"Ð"r7   c                óF   € R  pR p\         P                  ! V^È8¬  W3WC4      # )c                 óð   € \         P                  ! V 4      pV ^V,
          ,          W!,          ,           p\         P                  ! V 4      \        P                  ! \        V4      4      ,
          pW4,           pV# r_   )r|   r•  r  rQ   r  r	  )r˜   r\  r˜  ÚAÚBr‰  s   &&    r5   ró  Ú&gengamma_gen._entropy.<locals>.regularF  sM   € Ü—&’&˜“)ˆCØ�Q˜•W• ¥Õ'ˆAÜ—
’
˜1“¤§¢¤s¨1£v£Õ.ˆAØ•ˆAØˆHr7   c                 óâ  € \         P                  4       \        P                  ! V 4      ^,          ,
          \        P                  ! \        P                  ! V4      4      ,
          V R,          ^,          ,           V R,          ^Z,          ,
          \        P                  ! V 4      V R,          ^,          ,
          V R,          ^,          ,
          V R,          ^x,          ,           V,          ,           # )rÑ   r›  r÷  rö  rø  )r/  r  rQ   r  r	  )r˜   r\  s   &&r5   Ú
asymptoticÚ)gengamma_gen._entropy.<locals>.asymptoticM  s™   € ä—M‘M“O¤b§f¢f¨Q£i°¥kÕ1Ü—f’fœRŸVšV A›YÓ'õ(Ø+,¨c­6°1­*õ5Ø89¸3½Àµ{õCä—v’v˜a“y A s¥F¨A¥:Õ-°°Cµ¸µÕ;¸qÀ#½vÀs½lÕJÈAÕMõNð Or7   r=  )rD   r˜   r\  ró  rì  s   &&&  r5   r  Úgengamma_gen._entropyE  s(   € ò	ò	Oô �Š˜q C™x¨!¨°ÓEÐEr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rd   rm   ru   rý   ry   rö   r~   r„   rˆ   r,  r  r‘   r’   r“   s   @r5   rÄ  rÄ  õ  sH   ø‡ € ñò>"òò
-ò ò+ôò+ò4ò
4ò
#÷Fð Fr7   rÄ  Úgengammac                   óH   a € ] tR tRt o RtR tR tR tR tR t	R t
R	tV tR
# )Úgenhalflogistic_geniY  au  A generalized half-logistic continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `genhalflogistic` is:

.. math::

    f(x, c) = \frac{2 (1 - c x)^{1/(c-1)}}{[1 + (1 - c x)^{1/c}]^2}

for :math:`0 \le x \le 1/c`, and :math:`c > 0`.

`genhalflogistic` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úgenhalflogistic_gen._shape_infoo  r6  r7   c                ó,   € V P                   R V,          3# r8  r�  r÷  s   &&r5   r¥   Ú genhalflogistic_gen._get_supportr  s   € Ø�v‰v�s˜1•uˆ}Ðr7   c                óÄ   € R V,          p\         P                  ! ^W!,          ,
          4      pWC^,
          ,          pWT,          p^V,          ^V,           ^,          ,          # r8  ©rQ   r#  )rD   rt   r\  Úlimitr¿  Útmp0Útmp2s   &&&    r5   ru   Úgenhalflogistic_gen._pdfu  sJ   € ð �A•ˆÜ�jŠj˜˜1�3�ÓˆØ˜1•W�~ˆØ�xˆØ��v˜˜4� !�Õ#Ð#r7   c                ó˜   € R V,          p\         P                  ! ^W!,          ,
          4      pWC,          pR V,
          ^V,           ,          # r8  r÷  )rD   rt   r\  rø  r¿  rú  s   &&&   r5   ry   Úgenhalflogistic_gen._cdf~  s9   € Ø�A•ˆÜ�jŠj˜˜1�3�ÓˆØ�|ˆØ�D•˜Q˜t�VÕ$Ð$r7   c                óh   € R V,          ^R V,
          R V,           ,          V,          ,
          ,          # r8  r‹   rg  s   &&&r5   r„   Úgenhalflogistic_gen._ppf„  s'   € Ø�1�u�a˜#˜a�% # a¥%�¨1Õ,Õ,Õ-Ð-r7   c                óf   € ^^V,          ^,           \         P                  ! ^4      ,          ,
          # rD  rc  r÷  s   &&r5   r  Úgenhalflogistic_gen._entropy‡  s"   € Ø�A�a•C˜•Eœ2Ÿ6š6 !›9Õ$Õ$Ð$r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   r¥   ru   ry   r„   r  r‘   r’   r“   s   @r5   rñ  rñ  Y  s.   ø‡ € ñò*Eòò$ò%ò.÷%ð %r7   rñ  Úgenhalflogisticc                   ó†   a a€ ] tR tRt oRtR tR tV 3R ltR tR t	R ]
R	 4       4       tR
 tR tRR ltR tRtVtV ;t# )Úgenhyperbolic_geniŽ  u	  A generalized hyperbolic continuous random variable.

%(before_notes)s

See Also
--------
t, norminvgauss, geninvgauss, laplace, cauchy

Notes
-----
The probability density function for `genhyperbolic` is:

.. math::

    f(x, p, a, b) =
        \frac{(a^2 - b^2)^{p/2}}
        {\sqrt{2\pi}a^{p-1/2}
        K_p\Big(\sqrt{a^2 - b^2}\Big)}
        e^{bx} \times \frac{K_{p - 1/2}
        (a \sqrt{1 + x^2})}
        {(\sqrt{1 + x^2})^{1/2 - p}}

for :math:`x, p \in ( - \infty; \infty)`,
:math:`|b| < a` if :math:`p \ge 0`,
:math:`|b| \le a` if :math:`p < 0`.
:math:`K_{p}(.)` denotes the modified Bessel function of the second
kind and order :math:`p` (`scipy.special.kv`)

`genhyperbolic` takes ``p`` as a tail parameter,
``a`` as a shape parameter,
``b`` as a skewness parameter.

%(after_notes)s

The original parameterization of the Generalized Hyperbolic Distribution
is found in [1]_ as follows

.. math::

    f(x, \lambda, \alpha, \beta, \delta, \mu) =
       \frac{(\gamma/\delta)^\lambda}{\sqrt{2\pi}K_\lambda(\delta \gamma)}
       e^{\beta (x - \mu)} \times \frac{K_{\lambda - 1/2}
       (\alpha \sqrt{\delta^2 + (x - \mu)^2})}
       {(\sqrt{\delta^2 + (x - \mu)^2} / \alpha)^{1/2 - \lambda}}

for :math:`x \in ( - \infty; \infty)`,
:math:`\gamma := \sqrt{\alpha^2 - \beta^2}`,
:math:`\lambda, \mu \in ( - \infty; \infty)`,
:math:`\delta \ge 0, |\beta| < \alpha` if :math:`\lambda \ge 0`,
:math:`\delta > 0, |\beta| \le \alpha` if :math:`\lambda < 0`.

The location-scale-based parameterization implemented in
SciPy is based on [2]_, where :math:`a = \alpha\delta`,
:math:`b = \beta\delta`, :math:`p = \lambda`,
:math:`scale=\delta` and :math:`loc=\mu`

Moments are implemented based on [3]_ and [4]_.

For the distributions that are a special case such as Student's t,
it is not recommended to rely on the implementation of genhyperbolic.
To avoid potential numerical problems and for performance reasons,
the methods of the specific distributions should be used.

References
----------
.. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions
   on Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
   pp. 151-157, 1978. https://www.jstor.org/stable/4615705

.. [2] Eberlein E., Prause K. (2002) The Generalized Hyperbolic Model:
    Financial Derivatives and Risk Measures. In: Geman H., Madan D.,
    Pliska S.R., Vorst T. (eds) Mathematical Finance - Bachelier
    Congress 2000. Springer Finance. Springer, Berlin, Heidelberg.
    :doi:`10.1007/978-3-662-12429-1_12`

.. [3] Scott, David J, WÃ¼rtz, Diethelm, Dong, Christine and Tran,
   Thanh Tam, (2009), Moments of the generalized hyperbolic
   distribution, MPRA Paper, University Library of Munich, Germany,
   https://EconPapers.repec.org/RePEc:pra:mprapa:19081.

.. [4] E. Eberlein and E. A. von Hammerstein. Generalized hyperbolic
   and inverse Gaussian distributions: Limiting cases and approximation
   of processes. FDM Preprint 80, April 2003. University of Freiburg.
   https://freidok.uni-freiburg.de/fedora/objects/freidok:7974/datastreams/FILE1/content

%(example)s

c                óÐ   € \         P                  ! \         P                  ! V4      V8  V^ 8¬  4      \         P                  ! \         P                  ! V4      V8*  V^ 8  4      ,          # r  )rQ   Úlogical_andr	  )rD   rH  r˜   r™   s   &&&&r5   rd   Úgenhyperbolic_gen._argcheckè  sH   € Ü—’œrŸvšv a›y¨1™}¨a°1©fÓ5Ü—.’.¤§¢¨£¨a¡°°Q±Ó7õ8ð 	9r7   c                óú   € \        R R\        P                  ) \        P                  3R4      p\        RR^ \        P                  3R4      p\        RR\        P                  ) \        P                  3R4      pWV.# )rH  Fr˜   r™   r4  ri   rj   )rD   Úipr£  r¤  s   &   r5   rm   Úgenhyperbolic_gen._shape_infoì  sb   € Ü˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆÜ˜˜U Q¬¯© K°Ó?ˆÜ˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆØ˜ˆ|Ðr7   c                ó&   <€ \         SV `  VRR7      # )rM   r…  )rM   rM   r£   ra  rb  s   &&€r5   r×  Úgenhyperbolic_gen._fitstartò  s   ø€ ô ‰wÑ  ¨KÐ Ó8Ð8r7   c                ó@   € \         P                  R  4       pV! WW44      # )c                 ó0   € \         P                  ! WW#4      # rO   )r   Úgenhyperbolic_logpdf©rt   rH  r˜   r™   s   &&&&r5   Ú_logpdf_singleÚ1genhyperbolic_gen._logpdf.<locals>._logpdf_singleú  s   € ä×.Ò.¨q°QÓ:Ð:r7   ©rQ   Ú	vectorize)rD   rt   rH  r˜   r™   r  s   &&&&& r5   rý   Úgenhyperbolic_gen._logpdf÷  s)   € ô 
�‰ñ	;ó 
ð	;ñ ˜a AÓ)Ð)r7   c                ó@   € \         P                  R  4       pV! WW44      # )c                 ó0   € \         P                  ! WW#4      # rO   )r   Úgenhyperbolic_pdfr  s   &&&&r5   Ú_pdf_singleÚ+genhyperbolic_gen._pdf.<locals>._pdf_single  s   € ä×+Ò+¨A°!Ó7Ð7r7   r  )rD   rt   rH  r˜   r™   r  s   &&&&& r5   ru   Úgenhyperbolic_gen._pdf   s)   € ô 
�‰ñ	8ó 
ð	8ñ ˜1 Ó&Ð&r7   c                óP   € \         P                  ! V \         P                  .R 7      # )©Úotypes©rQ   r  Úfloat64)r˜  s   &r5   r  Úgenhyperbolic_gen.<lambda>  s   € ”"—,’,˜t¬R¯Z©Z¨LÕ9r7   c           	     ó8  € \         P                  ! W#V.\        4      P                  P	                  \        P
                  4      p\        P                  ! \        RV4      p\         P                  ! W4,           W4,
          ,          4      pWG,          \        P                  ! V^,           V4      ,          \        P                  ! W'4      ,          pRp	^ p
Yu;8  d   V8  dJ   M MF\        P                  ! W`VWšR7      ^ ,          \        P                  ! WhVWšR7      ^ ,          ,           pM \        P                  ! W`VWšR7      ^ ,          p\         P                  ! V4      '       d    Rp\        P                   ! V\"        ^R7       \%        R\'        RV4      4      # )z¨
Integrate the pdf of the genhyberbolic distribution from x0 to x1.
This is a private function used by _cdf() and _sf() only; either x0
will be -inf or x1 will be inf.
Ú_genhyperbolic_pdfru  )ÚepsrelÚepsabszdInfinite values encountered in scipy.special.kve. Values replaced by NaN to avoid incorrect results.r³  r•   r–   )rQ   Úarrayr  ÚctypesÚdata_asÚc_void_pr   Úfrom_cythonr   r'  r|   Úkvr   ÚquadÚisnanrµ  r¶  r·  ÚmaxrR  )r|  rí  rH  r˜   r™   Ú	user_dataÚllcr  r&  r$  r%  ÚintgrlrZ   s   &&&&&        r5   Ú_integrate_pdfÚ genhyperbolic_gen._integrate_pdf  s5  € ô —H’H˜a A˜Y¬Ó.×5Ñ5×=Ñ=¼f¿o¹oÓNˆ	Ü×*Ò*¬6Ð3GØ+4ó6ˆä�GŠG�Q•U˜Q�U•OÓ$ˆØ�s”R—U’U˜1˜q�5 !“_Õ$¤r§u¢u¨Q£{Õ2ˆØˆØˆØŽ>�r�>ô  —n’n S¨dØ,2ôCØCDõFä!Ÿš s°"Ø.4ôEØEFõHõH‰Fô
 —^’^ C¨RØ+1ôBØBCõEˆFä�8Š8�F×ÒðHˆCä�MŠM˜#œ~¸!Õ<Ü�3œ˜C Ó(Ó)Ð)r7   c                óF   € V P                  \        P                  ) WW44      # rO   ©r2  rQ   rk   ©rD   rt   rH  r˜   r™   s   &&&&&r5   ry   Úgenhyperbolic_gen._cdf.  s   € Ø×"Ñ"¤B§F¡F 7¨A°!Ó7Ð7r7   c                óF   € V P                  V\        P                  W#V4      # rO   r5  r6  s   &&&&&r5   r~   Úgenhyperbolic_gen._sf1  s   € Ø×"Ñ" 1¤b§f¡f¨a°AÓ6Ð6r7   c                óx  € \         P                  ! V^4      \         P                  ! V^4      ,
          p\         P                  ! VR4      p\         P                  ! VR4      p\        P                  VVVVVR7      p	\        P                  WER7      p
W9,          \         P
                  ! V	4      V
,          ,           # )rÑ   r£   )rH  r™   r.   rô   rõ   r'  r#  )rQ   Úfloat_powerÚgeninvgaussr)  r/  r'  )rD   rH  r˜   r™   rô   rõ   rû  rü  rý  ÚgigÚnormsts   &&&&&&     r5   rö   Úgenhyperbolic_gen._rvs4  s’   € ô
 �^Š^˜A˜qÓ!¤B§N¢N°1°aÓ$8Õ8ˆä�^Š^˜B Ó$ˆä�^Š^˜B Ó&ˆÜ�o‰oØØØØØ%ð ó ˆô —‘˜t�Ó?ˆà�wœŸš ›¨Õ.Õ.Ð.r7   c                óˆ  a€ \         P                  ! WV4      w  rp\         P                  ! V^4      \         P                  ! V^4      ,
          p\         P                  ! VR4      p\         P                  ! ^^4      \         P                  ! VR4      ,          p\         P                  ! ^ ^^4      pVP	                  VP
                  RVP                  ,          ,           4      p\        P                  ! W,           V4      w  orxršV3R lWxWš3 4       w  r¼rÞW5,          V,          pW[,          \         P                  ! V^4      \         P                  ! V^4      ,          V\         P                  ! V^4      ,
          ,          ,           p\         P                  ! V^4      \         P                  ! V^4      ,          V^V,          V,          \         P                  ! SR4      ,          ,
          ^\         P                  ! V^4      ,          ,           ,          ^V,          \         P                  ! V^4      ,          V\         P                  ! V^4      ,
          ,          ,           pV\         P                  ! VR4      ,          p\         P                  ! V^4      \         P                  ! V^4      ,          V^V	,          V,          \         P                  ! SR4      ,          ,
          ^V,          \         P                  ! V^4      ,          \         P                  ! SR4      ,          ,           ^\         P                  ! V^4      ,          ,
          ,          \         P                  ! V^4      \         P                  ! V^4      ,          ^V,          ^V,          V,          \         P                  ! SR4      ,          ,
          ^\         P                  ! V^4      ,          ,           ,          ,           ^\         P                  ! V^4      ,          V,          ,           pV\         P                  ! VR4      ,          ^,
          pVVVV3# )rÑ   r£   c              3   ó4   <"  € T F  qS,          x € K  	  R # 5irO   r‹   )Ú.0r™   Úb0s   & €r5   Ú	<genexpr>Ú+genhyperbolic_gen._stats.<locals>.<genexpr>U  s   øé € Ð;Ñ*: Q˜bŸ&š&Ó*:ùs   ƒr  r_   r<  r_  rw  )	rQ   rE  r;  Úlinspacer°  Úshaperƒ  r|   r+  )rD   rH  r˜   r™   rû  rü  ÚintegersÚb1Úb2Úb3Úb4Úr1Úr2Úr3Úr4rì  r  Úm3erj  Úm4erk  rC  s   &&&&                 @r5   r   Úgenhyperbolic_gen._statsI  s  ø€ ô ×%Ò% a¨AÓ.‰ˆˆaÜ�^Š^˜A˜qÓ!¤B§N¢N°1°aÓ$8Õ8ˆÜ�^Š^˜B Ó$ˆÜ�^Š^˜A˜qÓ!¤B§N¢N°2°sÓ$;Õ;ˆÜ—;’;˜q ! QÓ'ˆà×#Ñ# H§N¡N°T¸A¿F¹Fµ]Õ$BÓCˆÜŸUšU 1¥<°Ó4ÑˆˆB�BÜ;¨2°2Ñ*:Ó;‰ˆ�à�F�R�Kˆà�G”b—n’n Q¨Ó*¬R¯^ª^¸BÀÓ-BÕBØ”"—.’.  QÓ'Õ'õ)õ )ð 	
ô
 �NŠN˜1˜aÓ ¤2§>¢>°"°aÓ#8Õ8Ø�!�b•&˜2•+¤§¢¨r°2Ó 6Õ6Õ6Ø”—’  AÓ&Õ&õ'õ(ð ��E”B—N’N 2 qÓ)Õ)Ø”"—.’.  QÓ'Õ'õ)õ)ð 	ð ”"—.’.  GÓ,Õ,ˆä�NŠN˜1˜aÓ ¤2§>¢>°"°aÓ#8Õ8Ø�!�b•&˜2•+¤§¢¨r°3Ó 7Õ7Õ7Ø��V”b—n’n R¨Ó+Õ+¬b¯nªn¸RÀÓ.EÕEõFà”—’  AÓ&Õ&õ'õ(ô �NŠN˜1˜aÓ ¤2§>¢>°"°aÓ#8Õ8Ø��V�b˜2•g •l¤R§^¢^°B¸Ó%<Õ<Õ<Ø”—’  AÓ&Õ&õ'õ(õ	(ð ”—’˜r 1Ó%Õ%¨Õ*õ+ð 	ð ”"—.’.  BÓ'Õ'¨!Õ+ˆà�!�Q˜ˆzÐr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rd   rm   r×  rý   ru   Ústaticmethodr2  ry   r~   rö   r   r‘   r’   r  r   s   @@r5   r  r  Ž  s[   ù‡ € ñWòr9òõ9ò
*ò'ñ :Øñ*ó ó :ð*ò@8ò7ô/÷*'ò 'r7   r  Úgenhyperbolicc                   óT   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tRtV tR# )Úgompertz_geniv  aE  A Gompertz (or truncated Gumbel) continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `gompertz` is:

.. math::

    f(x, c) = c \exp(x) \exp(-c (e^x-1))

for :math:`x \ge 0`, :math:`c > 0`.

`gompertz` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úgompertz_gen._shape_infoŒ  r6  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r`  s   &&&r5   ru   Úgompertz_gen._pdf�  r™  r7   c                ó€   € \         P                  ! V4      V,           V\        P                  ! V4      ,          ,
          # rO   r  r`  s   &&&r5   rý   Úgompertz_gen._logpdf“  s%   € Ü�vŠv�a‹y˜1�}˜q¤2§8¢8¨A£;�Õ.Ð.r7   c                óh   € \         P                  ! V) \         P                  ! V4      ,          4      ) # rO   r=  r`  s   &&&r5   ry   Úgompertz_gen._cdf–  s#   € Ü—’˜!˜œbŸhšh q›kÕ)Ó*Ð*Ð*r7   c                ót   € \         P                  ! RV,          \         P                  ! V) 4      ,          4      # rš  r_  rg  s   &&&r5   r„   Úgompertz_gen._ppf™  s$   € Ü�xŠx˜˜q�¤2§8¢8¨Q¨B£<Õ/Ó0Ð0r7   c                óf   € \         P                  ! V) \        P                  ! V4      ,          4      # rO   r¡  r`  s   &&&r5   r~   Úgompertz_gen._sfœ  s    € Ü�vŠv�q�bœ2Ÿ8š8 A›;Õ&Ó'Ð'r7   c                óf   € \         P                  ! \        P                  ! V4      ) V,          4      # rO   r¤  ©rD   rH  r\  s   &&&r5   rˆ   Úgompertz_gen._isfŸ  s   € Ü�xŠxœŸš ›˜
 1�Ó%Ð%r7   c                ó’   € R \         P                  ! V4      ,
          \        P                  P	                  V4      V,          ,
          # r8  )rQ   r  r|   Ú_ufuncsÚ_scaled_exp1r÷  s   &&r5   r  Úgompertz_gen._entropy¢  s-   € Ø”R—V’V˜A“Y�¤§¡×!8Ñ!8¸Ó!;¸AÕ!=Õ=Ð=r7   r‹   N©rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   rˆ   r  r‘   r’   r“   s   @r5   rW  rW  v  s8   ø‡ € ñò*Eò*ò/ò+ò1ò(ò&÷>ð >r7   rW  Úgompertzc                 óà   € \         P                  ! V 4      p \         P                  ! V4      pVP                  4       p\         P                  ! W,
          4      p\         P                  ! WR 7      # ))Úweights)rQ   r#  r.  rÓ   Úaverage)rt   Ú
logweightsÚmaxlogwrn  s   &&  r5   Ú_average_with_log_weightsrr  ©  sI   € Ü
�
Š
�1‹€AÜ—’˜JÓ'€JØ�n‰nÓ€GÜ�fŠf�ZÕ)Ó*€GÜ�:Š:�aÔ)Ð)r7   c                   ó†   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR t]]! ]4      R 4       4       tRtV tR# )Úgumbel_r_geni±  aÐ  A right-skewed Gumbel continuous random variable.

%(before_notes)s

See Also
--------
gumbel_l, gompertz, genextreme

Notes
-----
The probability density function for `gumbel_r` is:

.. math::

    f(x) = \exp(-(x + e^{-x}))

for real :math:`x`.

The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
distribution.  It is also related to the extreme value distribution,
log-Weibull and Gompertz distributions.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úgumbel_r_gen._shape_infoÍ  r¼   r7   c                óL   € \         P                  ! V P                  V4      4      # rO   r.  r¿   s   &&r5   ru   Úgumbel_r_gen._pdfÐ  ó   € ä�vŠv�d—l‘l 1“oÓ&Ð&r7   c                ó@   € V) \         P                  ! V) 4      ,
          # rO   r7  r¿   s   &&r5   rý   Úgumbel_r_gen._logpdfÔ  s   € Øˆr”B—F’F˜A˜2“J�Ðr7   c                óZ   € \         P                  ! \         P                  ! V) 4      ) 4      # rO   r7  r¿   s   &&r5   ry   Úgumbel_r_gen._cdf×  s   € Ü�vŠv”r—v’v˜q˜b“z�kÓ"Ð"r7   c                ó2   € \         P                  ! V) 4      ) # rO   r7  r¿   s   &&r5   r  Úgumbel_r_gen._logcdfÚ  s   € Ü—’˜�r“
ˆ{Ðr7   c                óZ   € \         P                  ! \         P                  ! V4      ) 4      ) # rO   rc  rÉ   s   &&r5   r„   Úgumbel_r_gen._ppfÝ  s   € Ü—’œŸš˜q›	�zÓ"Ð"Ð"r7   c                ó\   € \         P                  ! \        P                  ! V) 4      ) 4      ) # rO   r  r¿   s   &&r5   r~   Úgumbel_r_gen._sfà  s    € Ü—’œ"Ÿ&š& ! ›*˜Ó%Ð%Ð%r7   c                ó\   € \         P                  ! \         P                  ! V) 4      ) 4      ) # rO   ©rQ   r  ré  r¢  s   &&r5   rˆ   Úgumbel_r_gen._isfã  s    € Ü—’œŸš ! ›�}Ó%Ð%Ð%r7   c                óî   € \         \        P                  \        P                  ,          R ,          ^\        P                  ! ^4      ,          \        P                  ^,          ,          \        ,          R3# )rJ  rc  ©r#   rQ   r  r'  r$   rl   s   &r5   r   Úgumbel_r_gen._statsæ  s?   € Ü”r—u‘uœRŸU™U•{ 3•¨¬2¯7ª7°1«:­´b·e±e¸QµhÕ(>ÄÕ(GÈÐOÐOr7   c                ó   € \         R ,           # r8  r¿  rl   s   &r5   r  Úgumbel_r_gen._entropyé  s   € ä˜�{Ðr7   c                óÀ  aaa€ \        V SW#4      w  orEV3R  lpVe   TpV! V4      oSV3# Ve   VoVV3R loMV3R loVP                  R^4      pV^,          V^,          r©V3R lpV! Wš4      '       g1   V	^ 8”  g   V
\        P                  8  d   V	^,          p	V
^,          p
K>  \        P
                  ! SWš3RRR7      pVP                  pVe   TMV! V4      oSV3# )c                 ó˜   <€ V ) \         P                  ! S) V ,          4      \        P                  ! \	        S4      4      ,
          ,          # rO   )r|   ró  rQ   r  rç  )r.   rE   s   &€r5   Úget_loc_from_scaleÚ,gumbel_r_gen.fit.<locals>.get_loc_from_scaleú  s1   ø€ Ø�6œRŸ\š\¨4¨%°%­-Ó8¼2¿6º6Ä#ÀdÃ)Ó;LÕLÕMÐMr7   c                 óÖ   <€ SS,
          \         P                  ! SS,
          V ,          4      ,          S,           p\        S4      SV ,           ,          pVP                  4       V,
          # rO   )rQ   rÓ   rç  rè  )r.   Úterm1Úterm2rE   r-   s   &  €€r5   r˜  Úgumbel_r_gen.fit.<locals>.func  sK   ø€ Ø  4�Z¬2¯6ª6°3¸µ:ÀÕ2FÓ+GÕGÈ$ÕN�EÜ ›I¨¨u­Õ5�EØ Ÿ9™9›;¨Õ.Ð.r7   c                 ón   <€ S) V ,          p\        SVR 7      pSP                  4       V,
          V ,
          # ))rp  )rr  r&  )r.   ÚsdataÚwavgrE   s   &  €r5   r˜  r“    s0   ø€ Ø!˜E E�M�EÜ4°TÀeÔL�DØŸ9™9›;¨Õ-°Õ5Ð5r7   r.   c                 óv   <€ \         P                  ! S! V 4      4      \         P                  ! S! V4      4      8g  # rO   rP   )rS   rT   r˜  s   &&€r5   rU   Ú0gumbel_r_gen.fit.<locals>.interval_contains_root"  s-   ø€ äŸš¡ V£Ó-ÜŸš¡ V£Ó-ñ.ð /r7   rO  )rQ  Úrtolrx  )rR  r<   rQ   rk   r   r*   rS  )rD   rE   rF   r4   r  r  rŽ  r.   Úbrack_startrS   rT   rU   Úresr˜  r-   s   &f*,         @@r5   rB   Úgumbel_r_gen.fití  s÷   ú€ ô 9¸¸tØ9=óEÑˆˆdõ	Nð Òð ˆEÙ$ UÓ+ˆCð\ �EˆzÐðU ÒØ�÷/õ6ð Ÿ(™( 7¨AÓ.ˆKØ(¨1�_¨k¸A­o�Fõ
/ñ .¨f×=Ò=Ø œ
 f¬r¯v©v¤oØ˜!•�Ø˜!•’ä×&Ò& t°fÐ5EØ,1¸ô?ˆCà—H‘HˆEØÒ*‘$Ñ0BÀ5Ó0IˆCØ�EˆzÐr7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r  r„   r~   rˆ   r   r  rK   r   r   rB   r‘   r’   r“   s   @r5   rt  rt  ±  s`   ø‡ € ñò6ò'òò#òò#ò&ò&òPòð Ù˜MÓ*ñ@ó +ó ö@r7   rt  Úgumbel_rc                   ó†   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR t]]! ]4      R 4       4       tRtV tR# )Úgumbel_l_geni5  aÉ  A left-skewed Gumbel continuous random variable.

%(before_notes)s

See Also
--------
gumbel_r, gompertz, genextreme

Notes
-----
The probability density function for `gumbel_l` is:

.. math::

    f(x) = \exp(x - e^x)

for real :math:`x`.

The Gumbel distribution is sometimes referred to as a type I Fisher-Tippett
distribution.  It is also related to the extreme value distribution,
log-Weibull and Gompertz distributions.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úgumbel_l_gen._shape_infoR  r¼   r7   c                óL   € \         P                  ! V P                  V4      4      # rO   r.  r¿   s   &&r5   ru   Úgumbel_l_gen._pdfU  ry  r7   c                ó<   € V\         P                  ! V4      ,
          # rO   r7  r¿   s   &&r5   rý   Úgumbel_l_gen._logpdfY  rû  r7   c                óZ   € \         P                  ! \        P                  ! V4      ) 4      ) # rO   r  r¿   s   &&r5   ry   Úgumbel_l_gen._cdf\  s   € Ü—’œ"Ÿ&š& ›)˜Ó$Ð$Ð$r7   c                óZ   € \         P                  ! \        P                  ! V) 4      ) 4      # rO   ©rQ   r  r|   ré  rÉ   s   &&r5   r„   Úgumbel_l_gen._ppf_  s   € Ü�vŠv”r—x’x  “|�mÓ$Ð$r7   c                ó0   € \         P                  ! V4      ) # rO   r7  r¿   s   &&r5   r
  Úgumbel_l_gen._logsfb  rH  r7   c                óX   € \         P                  ! \         P                  ! V4      ) 4      # rO   r7  r¿   s   &&r5   r~   Úgumbel_l_gen._sfe  ó   € Ü�vŠv”r—v’v˜a“y�jÓ!Ð!r7   c                óX   € \         P                  ! \         P                  ! V4      ) 4      # rO   rc  r¿   s   &&r5   rˆ   Úgumbel_l_gen._isfh  r¯  r7   c                óð   € \         ) \        P                  \        P                  ,          R ,          R\        P                  ! ^4      ,          \        P                  ^,          ,          \        ,          R3# )rJ  éôÿÿÿrc  rˆ  rl   s   &r5   r   Úgumbel_l_gen._statsk  sF   € ÜˆwœŸ™œbŸe™e� C�Ø”2—7’7˜1“:�~œbŸe™e Q�hÕ&¬Õ/°ð8ð 	8r7   c                ó   € \         R ,           # r8  r¿  rl   s   &r5   r  Úgumbel_l_gen._entropyo  s   € Ü˜�{Ðr7   c                ó®   € VP                  R 4      e   VR ,          ) VR &   \        P                  ! \        P                  ! V4      ) .VO5/ VB w  rEV) V3# )r  )r<   r�  rB   rQ   r#  )rD   rE   rF   r4   Úloc_rÚscale_rs   &&*,  r5   rB   Úgumbel_l_gen.fitr  sT   € ð �8‰8�FÓÒ'Ø  �L˜=ˆD�‰LÜ"Ÿ,š,¬¯
ª
°4Ó(8Ð'8ÐH¸4ÒHÀ4ÑH‰ˆØˆv�wˆÐr7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r
  r~   rˆ   r   r  rK   r   r   rB   r‘   r’   r“   s   @r5   rŸ  rŸ  5  s]   ø‡ € ñò8ò'òò%ò%òò"ò"ò8òð Ù˜MÓ*ñó +ó ör7   rŸ  Úgumbel_lc                   óŒ   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 tR t]]! ]4      V 3R l4       4       tRtVtV ;t# )Úhalfcauchy_geni†  zãA Half-Cauchy continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `halfcauchy` is:

.. math::

    f(x) = \frac{2}{\pi (1 + x^2)}

for :math:`x \ge 0`.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úhalfcauchy_gen._shape_infoš  r¼   r7   c                óX   € R \         P                  ,          RW,          ,           ,          # r  r`  r¿   s   &&r5   ru   Úhalfcauchy_gen._pdf�  s   € à”2—5‘5�y˜#˜a�c�'Õ"Ð"r7   c                óš   € \         P                  ! R \         P                  ,          4      \        P                  ! W,          4      ,
          # rr  ©rQ   r  r  r|   ré  r¿   s   &&r5   rý   Úhalfcauchy_gen._logpdf¡  s(   € Ü�vŠv�cœ"Ÿ%™%•iÓ ¤2§8¢8¨A­C£=Õ0Ð0r7   c                óf   € R \         P                  ,          \         P                  ! V4      ,          # rr  rÛ  r¿   s   &&r5   ry   Úhalfcauchy_gen._cdf¤  s   € Ø”2—5‘5�yœŸš 1›Õ%Ð%r7   c                óf   € \         P                  ! \         P                  ^,          V,          4      # rD  ©rQ   Útanr  rÉ   s   &&r5   r„   Úhalfcauchy_gen._ppf§  s   € Ü�vŠv”b—e‘e˜A•g˜a•iÓ Ð r7   c                óh   € R \         P                  ,          \         P                  ! ^V4      ,          # rr  )rQ   r  r  r¿   s   &&r5   r~   Úhalfcauchy_gen._sfª  s    € Ø”2—5‘5�yœ2Ÿ:š: a¨Ó+Õ+Ð+r7   c                ót   € R \         P                  ! \         P                  V,          ^,          4      ,          # r8  rÈ  r¢  s   &&r5   rˆ   Úhalfcauchy_gen._isf­  s"   € Ø”2—6’6œ"Ÿ%™% �' !�)Ó$Õ$Ð$r7   c                ó~   € \         P                  \         P                  \         P                  \         P                  3# rO   rE  rl   s   &r5   r   Úhalfcauchy_gen._stats°  r  r7   c                óX   € \         P                  ! ^\         P                  ,          4      # rD  r  rl   s   &r5   r  Úhalfcauchy_gen._entropy³  r  r7   c                ó*  <€ VP                  R R4      '       d   \        S
V `  ! V.VO5/ VB # \        WW#4      w  rp\        P
                  ! V4      pVe&   Wd8  d   \        RV\        P                  R7      hTpMTpR pVe   Tp	Wy3# V! Wq4      p	Wy3# )rE  FÚ
halfcauchyrÛ  c                 ó  aa€ W,
          pVP                   o\        P                  ! V4      oVV3R  lp\        P                  ! R4      P                  R,          p\        W4\        P                  ! V4      3R7      pVP                  # )c                 óz   <€ V ^,          S,           p^\         P                  ! SV,          4      ,          S,
          # rD  ©rQ   rè  )r.   Údenominatorrc   Úshifted_data_squareds   & €€r5   Úfun_to_solveÚ<halfcauchy_gen.fit.<locals>.find_scale.<locals>.fun_to_solveÐ  s1   ø€ Ø# Q�hÐ)=Õ=�Øœ2Ÿ6š6Ð"6°{Õ"BÓCÕCÀaÕGÐGr7   r–   r£   ©rQ  )rô   rQ   ÚsquareÚfinfoÚtinyr*   r.  rS  )r-   rE   Úshifted_datarÚ  Úsmallr›  rc   rÙ  s   &&    @@r5   Ú
find_scaleÚ&halfcauchy_gen.fit.<locals>.find_scaleË  sc   ù€ Ø�:ˆLØ—	‘	ˆAÜ#%§9¢9¨\Ó#:Ð öHô —H’H˜S“M×&Ñ&¨Õ+ˆEÜ˜l¼B¿FºFÀ<Ó<PÐ4QÔRˆCØ—8‘8ˆOr7   ©r2   r@   rB   rR  rQ   rR  rƒ  rk   )rD   rE   rF   r4   r  r  rS  r-   râ  r.   rØ  s   &&*,      €r5   rB   Úhalfcauchy_gen.fit¶  s­   ø€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä8¸Ø9=óEÑˆ�Fô —6’6˜$“<ˆØÒØŒä" <°tÄ2Ç6Á6ÔJÐJØ‰Cð ˆCò	ð ÒØˆEð ˆzÐñ ˜sÓ)ˆEàˆzÐr7   r‹   )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   rˆ   r   r  rK   r   r   rB   r‘   r’   r  r   s   @@r5   r½  r½  †  s]   ù‡ € ñò&ò#ò1ò&ò!ò,ò%ò.òð Ù˜MÓ*ô%ó +ó ÷%ð %r7   r½  rÔ  c                   óŒ   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 tR t]]! ]4      V 3R l4       4       tRtVtV ;t# )Úhalflogistic_geniã  aÃ  A half-logistic continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `halflogistic` is:

.. math::

    f(x) = \frac{ 2 e^{-x} }{ (1+e^{-x})^2 }
         = \frac{1}{2} \text{sech}(x/2)^2

for :math:`x \ge 0`.

%(after_notes)s

References
----------
.. [1] Asgharzadeh et al (2011). "Comparisons of Methods of Estimation for the
       Half-Logistic Distribution". Selcuk J. Appl. Math. 93-108.

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úhalflogistic_gen._shape_infoý  r¼   r7   c                óL   € \         P                  ! V P                  V4      4      # rO   r.  r¿   s   &&r5   ru   Úhalflogistic_gen._pdf   s   € ô �vŠv�d—l‘l 1“oÓ&Ð&r7   c                óª   € \         P                  ! ^4      V,
          R\        P                  ! \         P                  ! V) 4      4      ,          ,
          # rÐ   )rQ   r  r|   ré  rÓ   r¿   s   &&r5   rý   Úhalflogistic_gen._logpdf  s1   € Ü�vŠv�a‹y˜1�}˜r¤B§H¢H¬R¯VªV°Q°B«ZÓ$8Õ8Õ8Ð8r7   c                ó<   € \         P                  ! VR ,          4      # rr  )rQ   Útanhr¿   s   &&r5   ry   Úhalflogistic_gen._cdf  s   € Ü�wŠw�q˜•u‹~Ðr7   c                ó<   € ^\         P                  ! V4      ,          # rD  ©rQ   ÚarctanhrÉ   s   &&r5   r„   Úhalflogistic_gen._ppf  s   € Ø”—’˜A“�Ðr7   c                ó>   € ^\         P                  ! V) 4      ,          # rD  ©r|   Úexpitr¿   s   &&r5   r~   Úhalflogistic_gen._sf  s   € Ø”2—8’8˜Q˜B“<ÕÐr7   c                ó>   € \         P                  ! VR 8  VR R 4      # )r£   c                 ó>   € \         P                  ! R V ,          4      ) # r  ©r|   Úlogitrâ   s   &r5   r  Ú'halflogistic_gen._isf.<locals>.<lambda>  s   € ¬"¯(ª(°3¸µ7Ó*;Ñ);r7   c                 óJ   € ^\         P                  ! ^V ,
          4      ,          # rD  rò  râ   s   &r5   r  rý    s   € ¨¬2¯:ª:°a¸!µeÓ+<Ö)<r7   r=  rÉ   s   &&r5   rˆ   Úhalflogistic_gen._isf  s!   € Ü�Š˜q 3™w¨Ù;Ù<ó>ð 	>r7   c                ó   € V^ 8X  d   ^# V^8X  d   ^\         P                  ! ^4      ,          # V^8X  d-   \         P                  \         P                  ,          R,          # V^8X  d   ^	\        ,          # V^8X  d&   ^\         P                  ^,          ,          R,          # ^^\	        R^V,
          4      ,
          ,          \
        P                  ! V^,           4      ,          \
        P                  ! V^4      ,          # )r   r£  r·  rÒ   )rQ   r  r  r$   r¨  r|   r(  r¸  rb   s   &&r5   r,  Úhalflogistic_gen._munp  s©   € Ø�Œ6ÙØ�Œ6Ø”R—V’V˜A“Y•;ÐØ�Œ6Ü—5‘5œŸ™•;˜s•?Ð"Ø�Œ6Ø”V•8ˆOØ�Œ6Ø”R—U‘U˜A•X•: Õ$Ð$Ø�!”C˜˜Q˜q�S“M•/Õ"¤2§8¢8¨A¨a­C£=Õ0´·²¸¸A³Õ>Ð>r7   c                ó<   € ^\         P                  ! ^4      ,
          # rD  rc  rl   s   &r5   r  Úhalflogistic_gen._entropy#  re  r7   c                ó$  <€ VP                  R R4      '       d   \        S
V `  ! V.VO5/ VB # \        WW#4      w  rpR p\        P
                  ! V4      pVe&   Wt8  d   \        RV\        P                  R7      hTpMTpVe   TMV! W4      p	W‰3# )rE  Fc                 óÞ  € V P                   ^ ,          p\        P                  ! V ^ R7      p\        P                  ! ^V^,           4      V^,           ,          p^V,
          p^V,           pVRV,          V,          \        P                  ! We,          4      ,          ,
          pRV,          V,          pW1,
          p^\        P
                  ! VR,          VR,          ,          4      ,          p	^\        P
                  ! VR,          VR,          ^,          ,          4      ,          p
V	\        P                  ! V	^,          ^V,          V
,          ,           4      ,           ^V,          ,          pRp^pVP                  4       pWÜ8”  dh   V\        P                  ! V) V,          4      ,          pV^V,          VP                  4       ,          ,
          p\        VV,
          V,          4      pTpKm  V# )r   rO  r£   ºrM   NNr£  )rG  rQ   Úsortr¯  r  rè  r'  r&  r|   r÷  r	  )rE   r-   Ún_observationsÚsorted_datarH  rƒ   Úpp1rK  r©  ré  ÚCr.   r™  Úrelative_residualÚshifted_meanÚsum_termÚ	scale_news   &&               r5   râ  Ú(halflogistic_gen.fit.<locals>.find_scale/  sv  € ð "ŸZ™Z¨�]ˆNÜŸ'š' $¨QÔ/ˆKÜ—	’	˜!˜^¨aÕ/Ó0°.À1Õ2DÕEˆAØ�A•ˆAØ�a•%ˆCØ˜˜a� #�¬¯ª¨s­w«Õ7Õ7ˆEØ˜•7˜S•=ˆDØ%Õ+ˆKØ”B—F’F˜5 �9 {°2¥Õ6Ó7Õ7ˆAØ”B—F’F˜4 �8 k°"¥o°qÕ&8Õ8Ó9Õ9ˆAàœ"Ÿ'š' ! Q¥$¨¨^Õ);¸aÕ)?Õ"?Ó@Õ@Ø˜.Õ(õ*ˆEð ˆDØ !ÐØ&×+Ñ+Ó-ˆLð $Ô*Ø&¬¯ª°;°,¸uÕ2DÓ)EÕE�Ø(¨1¨^Õ+;¸h¿l¹l»nÕ+LÕL�	Ü$'¨°Õ):¸EÕ(AÓ$BÐ!Ø!’ØˆLr7   ÚhalflogisticrÛ  rä  )rD   rE   rF   r4   r  r  râ  rS  r-   r.   rØ  s   &&*,      €r5   rB   Úhalflogistic_gen.fit&  sž   ø€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä8¸Ø9=óEÑˆ�Fò	ôD —6’6˜$“<ˆØÒØŒä" >¸ÄRÇVÁVÔLÐLØ‰Cð ˆCð !Ò,‘±*¸TÓ2GˆàˆzÐr7   r‹   )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   rˆ   r,  r  rK   r   r   rB   r‘   r’   r  r   s   @@r5   rç  rç  ã  s]   ù‡ € ñò2ò'ò
9òòò ò>ò
?òð Ù˜MÓ*ô6ó +ó ÷6ð 6r7   rç  r  c                   ó–   a a€ ] tR tRt oRtR tRR ltR tR tR t	R t
R	 tR
 tR tR t]]! ]4      V 3R l4       4       tRtVtV ;t# )Úhalfnorm_genid  a  A half-normal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `halfnorm` is:

.. math::

    f(x) = \sqrt{2/\pi} \exp(-x^2 / 2)

for :math:`x >= 0`.

`halfnorm` is a special case of `chi` with ``df=1``.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úhalfnorm_gen._shape_infoz  r¼   r7   c                ó8   € \        VP                  VR 7      4      # rà  r  ró   s   &&&r5   rö   Úhalfnorm_gen._rvs}  s   € Ü�<×/Ñ/°TÐ/Ó:Ó;Ð;r7   c                ó¬   € \         P                  ! R \         P                  ,          4      \         P                  ! V) V,          R ,          4      ,          # rr  ©rQ   r'  r  rÓ   r¿   s   &&r5   ru   Úhalfnorm_gen._pdf€  s1   € ä�wŠw�sœ2Ÿ5™5•yÓ!¤"§&¢&¨!¨¨A­¨c­Ó"2Õ2Ð2r7   c                óŽ   € R \         P                  ! R\         P                  ,          4      ,          W,          R,          ,
          # ©r£   rÒ   r  r¿   s   &&r5   rý   Úhalfnorm_gen._logpdf„  s)   € Ø”R—V’V˜C¤§¡�IÓ&Õ&¨­¨S­Õ0Ð0r7   c                ód   € \         P                  ! V\        P                  ! ^4      ,          4      # rD  ©r|   r  rQ   r'  r¿   s   &&r5   ry   Úhalfnorm_gen._cdf‡  s   € Ü�vŠv�aœ"Ÿ'š' !›*•nÓ%Ð%r7   c                ó4   € \        ^V,           R,          4      # ro  rë   rÉ   s   &&r5   r„   Úhalfnorm_gen._ppfŠ  s   € Ü˜!˜A�#˜s�Ó#Ð#r7   c                ó&   € ^\        V4      ,          # rD  r  r¿   s   &&r5   r~   Úhalfnorm_gen._sf�  s   € Ø”8˜A“;�Ðr7   c                ó&   € \        V^,          4      # rD  r  r¢  s   &&r5   rˆ   Úhalfnorm_gen._isf�  s   € Ü˜˜1�‹~Ðr7   c                ó¼  € \         P                  ! R \         P                  ,          4      ^R \         P                  ,          ,
          \         P                  ! ^4      ^\         P                  ,
          ,          \         P                  ^,
          R,          ,          ^\         P                  ^,
          ,          \         P                  ^,
          ^,          ,          3# )rÒ   rS  ©rQ   r'  r  rl   s   &r5   r   Úhalfnorm_gen._stats“  sx   € Ü—’˜œBŸE™E�	Ó"Ø�#”b—e‘e•)•Ü—’˜“
˜AœbŸe™e�GÕ$¤b§e¡e¨A¥g°¥^Õ3Ø”2—5‘5˜•7•œRŸU™U 1�W q�LÕ(ð*ð 	*r7   c                ót   € R \         P                  ! \         P                  R,          4      ,          R ,           # r  r  rl   s   &r5   r  Úhalfnorm_gen._entropy™  s#   € Ø”2—6’6œ"Ÿ%™% �)Ó$Õ$ SÕ(Ð(r7   c                óT  <€ VP                  R R4      '       d   \        S	V `  ! V.VO5/ VB # \        WW#4      w  rp\        P
                  ! V4      pVe&   Wd8  d   \        RV\        P                  R7      hTpMTpVe   TpWx3# \        P                  ! V^VR7      R,          pWx3# )rE  FÚhalfnormrÛ  )ÚorderÚcenterr£   )
r2   r@   rB   rR  rQ   rR  rƒ  rk   rF  Úmoment)
rD   rE   rF   r4   r  r  rS  r-   r.   rØ  s
   &&*,     €r5   rB   Úhalfnorm_gen.fitœ  s±   ø€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä8¸Ø9=óEÑˆ�Fô —6’6˜$“<ˆàÒØŒä" :°TÄÇÁÔHÐHØ‰CàˆCàÒØˆEð ˆzÐô —L’L ¨Q°sÔ;¸SÕ@ˆEàˆzÐr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r„   r~   rˆ   r   r  rK   r   r   rB   r‘   r’   r  r   s   @@r5   r  r  d  sb   ù‡ € ñò*ô<ò3ò1ò&ò$òòò*ò)ð Ù˜MÓ*ôó +ó ÷ð r7   r  r.  c                   óT   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tRtV tR# )Úhypsecant_geniº  zõA hyperbolic secant continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `hypsecant` is:

.. math::

    f(x) = \frac{1}{\pi} \text{sech}(x)

for a real number :math:`x`.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úhypsecant_gen._shape_infoÎ  r¼   r7   c                óf   € R \         P                  \         P                  ! V4      ,          ,          # r8  )rQ   r  Úcoshr¿   s   &&r5   ru   Úhypsecant_gen._pdfÑ  s   € à”B—E‘Eœ"Ÿ'š' !›*Õ$Õ%Ð%r7   c                óŽ   € R \         P                  ,          \         P                  ! \         P                  ! V4      4      ,          # rr  ©rQ   r  rÜ  rÓ   r¿   s   &&r5   ry   Úhypsecant_gen._cdfÕ  s&   € Ø”2—5‘5�yœŸš¤2§6¢6¨!£9Ó-Õ-Ð-r7   c                óŽ   € \         P                  ! \         P                  ! \         P                  V,          R ,          4      4      # rr  ©rQ   r  rÉ  r  rÉ   s   &&r5   r„   Úhypsecant_gen._ppfØ  s&   € Ü�vŠv”b—f’fœRŸU™U 1�W S�[Ó)Ó*Ð*r7   c                ó�   € R \         P                  ,          \         P                  ! \         P                  ! V) 4      4      ,          # rr  r;  r¿   s   &&r5   r~   Úhypsecant_gen._sfÛ  s(   € Ø”2—5‘5�yœŸš¤2§6¢6¨1¨"£:Ó.Õ.Ð.r7   c                ó�   € \         P                  ! \         P                  ! \         P                  V,          R ,          4      4      ) # rr  r>  rÉ   s   &&r5   rˆ   Úhypsecant_gen._isfÞ  s)   € Ü—’”r—v’vœbŸe™e A�g c�kÓ*Ó+Ð+Ð+r7   c                ób   € ^ \         P                  \         P                  ,          ^,          ^ ^3# r  r`  rl   s   &r5   r   Úhypsecant_gen._statsá  s!   € Ø”"—%‘%œŸ™•+˜a•-  AÐ%Ð%r7   c                óX   € \         P                  ! ^\         P                  ,          4      # rD  r  rl   s   &r5   r  Úhypsecant_gen._entropyä  r  r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   ry   r„   r~   rˆ   r   r  r‘   r’   r“   s   @r5   r4  r4  º  s7   ø‡ € ñò&ò&ò.ò+ò/ò,ò&÷ð r7   r4  Ú	hypsecantc                   ó<   a € ] tR tRt o RtR tR tR tR tRt	V t
R# )	Úgausshyper_genië  a  A Gauss hypergeometric continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `gausshyper` is:

.. math::

    f(x, a, b, c, z) = C x^{a-1} (1-x)^{b-1} (1+zx)^{-c}

for :math:`0 \le x \le 1`, :math:`a,b > 0`, :math:`c` a real number,
:math:`z > -1`, and :math:`C = \frac{1}{B(a, b) F[2, 1](c, a; a+b; -z)}`.
:math:`F[2, 1]` is the Gauss hypergeometric function
`scipy.special.hyp2f1`.

`gausshyper` takes :math:`a`, :math:`b`, :math:`c` and :math:`z` as shape
parameters.

%(after_notes)s

References
----------
.. [1] Armero, C., and M. J. Bayarri. "Prior Assessments for Prediction in
       Queues." *Journal of the Royal Statistical Society*. Series D (The
       Statistician) 43, no. 1 (1994): 139-53. doi:10.2307/2348939

%(example)s

c                óF   € V^ 8„  V^ 8„  ,          W38H  ,          VR8„  ,          # )r   r  r‹   )rD   r˜   r™   r\  rÓ  s   &&&&&r5   rd   Úgausshyper_gen._argcheck  s%   € à�A‘˜!˜a™%Õ  A¡FÕ+¨q°2©vÕ6Ð6r7   c                ó  € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      p\        RR\        P                  ) \        P                  3R4      p\        RRR\        P                  3R4      pWW4.# )r˜   Fr™   r\  rÓ  r4  r  rj   )rD   r£  r¤  ry  Úizs   &    r5   rm   Úgausshyper_gen._shape_info  st   € Ü˜˜U Q¬¯© K°Ó@ˆÜ˜˜U Q¬¯© K°Ó@ˆÜ˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆÜ˜˜U R¬¯© L°.ÓAˆØ˜ÐÐr7   c                ó  € \         P                  ! W#4      \         P                  ! WBW#,           V) 4      ,          pR V,          WR ,
          ,          ,          R V,
          VR ,
          ,          ,          R WQ,          ,           V,          ,          # r8  ©r|   r©  Úhyp2f1)rD   rt   r˜   r™   r\  rÓ  Únormalization_constants   &&&&&& r5   ru   Úgausshyper_gen._pdf  sc   € Ü!#§¢¨£´·²¸1ÀÅÈÈÓ1KÕ!KÐØÐ)Õ)¨A°Bµ­KÕ7¸2À½6ÀQÈÅWÕ:MÕMØ˜�•9˜q•.õ!ð 	"r7   c                ó(  € \         P                  ! W,           V4      \         P                  ! W#4      ,          p\         P                  ! WBV,           W#,           V,           V) 4      p\         P                  ! WBW#,           V) 4      pWg,          V,          # rO   rQ  )	rD   rc   r˜   r™   r\  rÓ  rî  rK  rÈ  s	   &&&&&&   r5   r,  Úgausshyper_gen._munp  s`   € Ü�gŠg�a•c˜1‹o¤§¢¨£Õ-ˆÜ�iŠi˜˜Q�3 ¥ A¥¨ rÓ*ˆÜ�iŠi˜˜a�c A 2Ó&ˆØ�w˜�}Ðr7   r‹   N)rŒ   r�   rŽ   r�   r�   rd   rm   ru   r,  r‘   r’   r“   s   @r5   rJ  rJ  ë  s$   ø‡ € ñò@7ò ò"÷
ð r7   rJ  Ú
gausshyperc                   óv   a € ] tR tRt o Rt]P                  tR tR t	R t
R tR tR tR	 tRR
 ltR tRtV tR# )Úinvgamma_geni&  a  An inverted gamma continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `invgamma` is:

.. math::

    f(x, a) = \frac{x^{-a-1}}{\Gamma(a)} \exp(-\frac{1}{x})

for :math:`x >= 0`, :math:`a > 0`. :math:`\Gamma` is the gamma function
(`scipy.special.gamma`).

`invgamma` takes ``a`` as a shape parameter for :math:`a`.

`invgamma` is a special case of `gengamma` with ``c=-1``, and it is a
different parameterization of the scaled inverse chi-squared distribution.
Specifically, if the scaled inverse chi-squared distribution is
parameterized with degrees of freedom :math:`\nu` and scaling parameter
:math:`\tau^2`, then it can be modeled using `invgamma` with
``a=`` :math:`\nu/2` and ``scale=`` :math:`\nu \tau^2/2`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r3  rj   rl   s   &r5   rm   Úinvgamma_gen._shape_infoF  r6  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r9  s   &&&r5   ru   Úinvgamma_gen._pdfI  r™  r7   c                óž   € V^,           ) \         P                  ! V4      ,          \        P                  ! V4      ,
          RV,          ,
          # r&  ©rQ   r  r|   r  r9  s   &&&r5   rý   Úinvgamma_gen._logpdfM  s1   € Ø�1•ˆvœŸš˜q›	Õ!¤B§J¢J¨q£MÕ1°C¸µEÕ9Ð9r7   c                ó>   € \         P                  ! VR V,          4      # r8  rE  r9  s   &&&r5   ry   Úinvgamma_gen._cdfP  s   € Ü�|Š|˜A˜s Q�wÓ'Ð'r7   c                ó<   € R \         P                  ! W!4      ,          # r8  r’  rA  s   &&&r5   r„   Úinvgamma_gen._ppfS  s   € Ø”R—_’_ QÓ*Õ*Ð*r7   c                ó>   € \         P                  ! VR V,          4      # r8  rA  r9  s   &&&r5   r~   Úinvgamma_gen._sfV  s   € Ü�{Š{˜1˜c A�gÓ&Ð&r7   c                ó<   € R \         P                  ! W!4      ,          # r8  r~  rA  s   &&&r5   rˆ   Úinvgamma_gen._isfY  s   € Ø”R—^’^ AÓ)Õ)Ð)r7   c                óŒ  € \         P                  ! V^8„  VR \        P                  R7      p\         P                  ! V^8„  VR \        P                  R7      pRRreRV9   d-   \         P                  ! V^8„  VR \        P                  R7      pRV9   d-   \         P                  ! V^8„  VR \        P                  R7      pW4WV3# )	rM   c                 ó"   € R V R ,
          ,          # r8  r‹   rÕ   s   &r5   r  Ú%invgamma_gen._stats.<locals>.<lambda>^  s   €  r¨Q°­V¦}r7   r  c                 óL   € R V R ,
          ^,          ,          V R,
          ,          # ©r–   rÒ   r‹   rÕ   s   &r5   r  rk  a  s   €  r¨Q°­V°a­KÕ'7¸1¸r½6Ö'Br7   Nrj  c                 óf   € R \         P                  ! V R,
          4      ,          V R,
          ,          # )r¬  rÒ   r£  rÇ  rÕ   s   &r5   r  rk  g  s   € ¨2´·²¸¸B½³Õ+?À1ÀrÅ6Ö+Jr7   rk  c                 óh   € R RV ,          R,
          ,          V R,
          ,          V R,
          ,          # )rJ  r§  g      &@r£  r¬  r‹   rÕ   s   &r5   r  rk  k  s$   € ¨2°°aµ¸#µÕ+>À!ÀbÅ&Õ+IÈQÐQSÍVÖ+Tr7   rð  )rD   r˜   rl  rª  r«  r{  r|  s   &&&    r5   r   Úinvgamma_gen._stats\  s©   € Ü�_Š_˜Q ™U AÙ4Ü(*¯©ô0ˆô �_Š_˜Q ™U AÙBÜ(*¯©ô0ˆð �tˆBØ�'Œ>Ü—’  Q¡¨Ù!JÜ,.¯F©Fô4ˆBð �'Œ>Ü—’  Q¡¨Ù!TÜ,.¯F©Fô4ˆBð �rˆ~Ðr7   c                óH   € R  pR p\         P                  ! V^È8¬  WV4      pV# )c                 ó�   € W R ,           \         P                  ! V 4      ,          ,
          \         P                  ! V 4      ,           pV# r8  rœ  ©r˜   r‰  s   & r5   ró  Ú&invgamma_gen._entropy.<locals>.regularq  s-   € Ø˜•W¤§¢ q£	Õ)Õ)¬B¯JªJ°q«MÕ9ˆAØˆHr7   c                 óŒ  € ^^\         P                  ! V 4      ,          ,
          \         P                  ! ^4      ,           \         P                  ! \         P                  4      ,           ^,          RV R,          ,          ,           V R,          ^,          ,           V R,          ^Z,          ,
          V R,          ^x,          ,
          pV# )rM   çUUUUUUå?r›  rö  r÷  rø  r  rs  s   & r5   rì  Ú)invgamma_gen._entropy.<locals>.asymptoticu  s‚   € ð �aœŸš˜q›	•k•/¤B§F¢F¨1£IÕ-´·²´r·u±u³Õ=¸qÕ@Ø�q˜#•v•:õØ ! 3¥ r¥	õ*Ø,-¨s­F°2­Iõ6Ø89¸3½¸s½
õCˆAàˆHr7   r=  )rD   r˜   ró  rì  r‰  s   &&   r5   r  Úinvgamma_gen._entropyp  s)   € ò	ò	ô �OŠO˜A ™H a°WÓ=ˆØˆr7   r‹   N©Úmvsk)rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   ru   rý   ry   r„   r~   rˆ   r   r  r‘   r’   r“   s   @r5   rY  rY  &  sJ   ø‡ € ñð: "×4Ñ4€MòEò*ò:ò(ò+ò'ò*ô÷(ð r7   rY  Úinvgammac                   ó¼   a a€ ] tR tRt oRt]P                  tR tRR lt	R t
R tR tR tR	 tR
 tV 3R ltV 3R ltR t]! ]4      V 3R l4       tR tRtVtV ;t# )Úinvgauss_geniƒ  añ  An inverse Gaussian continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `invgauss` is:

.. math::

    f(x; \mu) = \frac{1}{\sqrt{2 \pi x^3}}
                \exp\left(-\frac{(x-\mu)^2}{2 \mu^2 x}\right)

for :math:`x \ge 0` and :math:`\mu > 0`.

`invgauss` takes ``mu`` as a shape parameter for :math:`\mu`.

%(after_notes)s

A common shape-scale parameterization of the inverse Gaussian distribution
has density

.. math::

    f(x; \nu, \lambda) = \sqrt{\frac{\lambda}{2 \pi x^3}}
                \exp\left( -\frac{\lambda(x-\nu)^2}{2 \nu^2 x}\right)

Using ``nu`` for :math:`\nu` and ``lam`` for :math:`\lambda`, this
parameterization is equivalent to the one above with ``mu = nu/lam``,
``loc = 0``, and ``scale = lam``.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``ppf`` and ``isf`` methods. [1]_

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# ©ry  Fr4  rj   rl   s   &r5   rm   Úinvgauss_gen._shape_info¯  r5  r7   c                ó*   € VP                  VR VR7      # ©r–   r³  ©Úwald©rD   ry  rô   rõ   s   &&&&r5   rö   Úinvgauss_gen._rvs²  s   € Ø× Ñ   S¨tÐ Ó4Ð4r7   c                ó
  € R \         P                  ! ^\         P                  ,          VR,          ,          4      ,          \         P                  ! R^V,          ,          W,          ^,
          ^,          ,          4      ,          # )r–   r£  r›  r  ©rD   rt   ry  s   &&&r5   ru   Úinvgauss_gen._pdfµ  sM   € ð ”2—7’7˜1œRŸU™U�7 1 c¥6�>Ó*Õ*¬2¯6ª6°$¸¸!½µ*¸a½dÀQ½hÈ½]Õ2JÓ+KÕKÐKr7   c                óü   € R\         P                  ! ^\         P                  ,          4      ,          R\         P                  ! V4      ,          ,
          W,          ^,
          ^,          ^V,          ,          ,
          # )r£   rS  r#  r  rˆ  s   &&&r5   rý   Úinvgauss_gen._logpdfº  sF   € Ø”B—F’F˜1œRŸU™U�7“OÕ# c¬"¯&ª&°«)¥mÕ3°qµt¸aµxÀ!µmÀQÀqÅSÕ6IÕIÐIr7   c                óD  € ^\         P                  ! V4      ,          p\        W1V,          ^,
          ,          4      p^V,          \        V) W,          ^,           ,          4      ,           pV\         P                  ! \         P                  ! WT,
          4      4      ,           # r_   )rQ   r'  rß   ré  rÓ   ©rD   rt   ry  rî  r˜   r™   s   &&&   r5   r  Úinvgauss_gen._logcdfÁ  sf   € Ø”"—'’'˜!“*�nˆÜ˜ "¥ q¥Õ)Ó*ˆØ��F”\ 3 $¨!­$°­(Õ"3Ó4Õ4ˆØ”2—8’8œBŸFšF 1¥5›MÓ*Õ*Ð*r7   c                óF  € ^\         P                  ! V4      ,          p\        W1V,          ^,
          ,          4      p^V,          \        V) W,          ^,           ,          4      ,           pV\         P                  ! \         P
                  ! WT,
          4      ) 4      ,           # r_   )rQ   r'  ré   rß   ré  rÓ   r�  s   &&&   r5   r
  Úinvgauss_gen._logsfÇ  sh   € Ø”"—'’'˜!“*�nˆÜ˜ �t a�xÕ(Ó)ˆØ��F”\ 3 $¨!­$°­(Õ"3Ó4Õ4ˆØ”2—8’8œRŸVšV A¥E›]˜NÓ+Õ+Ð+r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r“  rˆ  s   &&&r5   r~   Úinvgauss_gen._sfÍ  s   € Ü�vŠv�d—k‘k !Ó(Ó)Ð)r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r  rˆ  s   &&&r5   ry   Úinvgauss_gen._cdfÐ  ó   € Ü�vŠv�d—l‘l 1Ó)Ó*Ð*r7   c           	     óÖ  <€ \         P                  ! R R R R7      ;_uu_ 4        \         P                  ! W4      w  r\         P                  ! \        P
                  ! W^4      4      pVR8„  p\        P                  ! ^W,          ,
          W$,          ^4      W4&   \         P                  ! V4      p\        SV `%  W,          W%,          4      W5&   RRR4       V#   + '       g   i     X# ; i©rl  )rn  r®  ré  r£   N)
rQ   ro  rE  r#  rq   Ú_invgauss_ppfÚ_invgauss_isfr-  r@   r„   )rD   rt   ry  ÚppfÚi_wtÚi_nanrØ  s   &&&   €r5   r„   Úinvgauss_gen._ppfÓ  s«   ø€ Ü�[Š[ ¨xÀ×JÖJÜ×'Ò'¨Ó.‰EˆAÜ—*’*œS×.Ò.¨q°aÓ8Ó9ˆCØ�s‘7ˆDÜ×)Ò)¨!¨A­G­)°RµX¸qÓAˆC‰IÜ—H’H˜S“MˆEÜ™™ a¥h°µ	Ó:ˆC‰J÷ Kð ˆ
÷ KÖJð ˆ
ús   £B*CÃC(	c                ó®  <€ \         P                  ! R R R R7      ;_uu_ 4        \         P                  ! W4      w  r\        P                  ! W^4      pVR8„  p\        P
                  ! ^W,          ,
          W$,          ^4      W4&   \         P                  ! V4      p\        SV `!  W,          W%,          4      W5&   RRR4       V#   + '       g   i     X# ; ir—  )	rQ   ro  rE  rq   r™  r˜  r-  r@   rˆ   )rD   rt   ry  Úisfr›  rœ  rØ  s   &&&   €r5   rˆ   Úinvgauss_gen._isfÝ  s¢   ø€ Ü�[Š[ ¨xÀ×JÖJÜ×'Ò'¨Ó.‰EˆAÜ×#Ò# A¨1Ó-ˆCØ�s‘7ˆDÜ×)Ò)¨!¨A­G­)°RµX¸qÓAˆC‰IÜ—H’H˜S“MˆEÜ™™ a¥h°µ	Ó:ˆC‰J÷ Kð ˆ
÷ KÖJð ˆ
ús   £BCÃC	c                ó^   € WR ,          ^\         P                  ! V4      ,          ^V,          3# )r£  rÇ  )rD   ry  s   &&r5   r   Úinvgauss_gen._statsç  s#   € Ø�s•7˜AœbŸgšg b›k�M¨2¨b­5Ð0Ð0r7   c                ó~  <€ VP                  R R4      p\        V\        4      '       g,   \        V \        4      '       g   VP	                  4       R8X  d   \
        S	V `  ! V.VO5/ VB # \        WW#4      w  rrg Ve   Ve   \
        S	V `  ! V.VO5/ VB # \        P                  ! W,
          ^ 8  4      '       d   \        R^ \        P                  R7      hW,
          p\        P                  ! V4      pVf<   \        V4      \        P                  ! VR,          VR,          ,
          4      ,          pW‡,          pWVV3# )r0   r:   r;   ÚinvgaussrÛ  r  )r<   r>   r)   Úwald_genr=   r@   rB   rR  rQ   ræ  rƒ  rk   r&  rç  rè  )
rD   rE   rF   r4   r0   Úfshape_sr  r  Úfshape_nrØ  s
   &&*,     €r5   rB   Úinvgauss_gen.fitê  s
  ø€ à—‘˜( EÓ*ˆä�tœ\×*Ò*¬j¸¼x×.HÒ.HØ—<‘<“> TÔ)Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä'BÀ4ØCGó(OÑ$ˆ˜ð	ð Š<˜8Ò/Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3Ü�VŠV�D•K !‘O×$Ò$Ü˜z°¼"¿&¹&ÔAÐAà•;ˆDÜ—w’w˜t“}ˆHØŠ~Ü˜T›¤b§f¢f¨T°R­Z¸(Àb½.Õ-HÓ&IÕJ�ØÕ(ˆHØ˜vÐ%Ð%r7   c                ó6  € R\         P                  ! ^\         P                  ,          4      ,           ^\         P                  ! V4      ,          ,           p^V,          p\        P                  P                  V4      V,          pRV,          RV,          ,
          # )zF
Ref.: https://moser-isi.ethz.ch/docs/papers/smos-2012-10.pdf (eq. 9)
r–   r£   rS  )rQ   r  r  r|   rh  ri  )rD   ry  r˜   rI  r™   s   &&   r5   r  Úinvgauss_gen._entropy  sg   € ð ”—’˜œBŸE™E�	Ó"Õ" Q¬¯ª°«¥^Õ3ˆð ˆb�DˆÜ�J‰J×#Ñ# AÓ& qÕ(ˆØ�Q�w˜˜q�Õ Ð r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   rö   ru   rý   r  r
  r~   ry   r„   rˆ   r   r   rB   r  r‘   r’   r  r   s   @@r5   r}  r}  ƒ  sv   ù‡ € ñ(ðR "×4Ñ4€MòFô5òLò
Jò+ò,ò*ò+õõò1ñ ˜MÓ*ô&ó +ð&÷B!ò !r7   r}  r¤  c                   ód   a € ] tR tRt o RtR tR tR tR tR t	R t
RR
 ltR tR tR tRtV tR	# )Úgeninvgauss_geni  a  A Generalized Inverse Gaussian continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `geninvgauss` is:

.. math::

    f(x, p, b) = x^{p-1} \exp(-b (x + 1/x) / 2) / (2 K_p(b))

where ``x > 0``, `p` is a real number and ``b > 0``\([1]_).
:math:`K_p` is the modified Bessel function of second kind of order `p`
(`scipy.special.kv`).

%(after_notes)s

The inverse Gaussian distribution `stats.invgauss(mu)` is a special case of
`geninvgauss` with ``p = -1/2``, ``b = 1 / mu`` and ``scale = mu``.

Generating random variates is challenging for this distribution. The
implementation is based on [2]_.

References
----------
.. [1] O. Barndorff-Nielsen, P. Blaesild, C. Halgreen, "First hitting time
   models for the generalized inverse gaussian distribution",
   Stochastic Processes and their Applications 7, pp. 49--54, 1978.

.. [2] W. Hoermann and J. Leydold, "Generating generalized inverse Gaussian
   random variates", Statistics and Computing, 24(4), p. 547--557, 2014.

%(example)s

c                ó   € W8H  V^ 8„  ,          # r  r‹   ©rD   rH  r™   s   &&&r5   rd   Úgeninvgauss_gen._argcheckB  s   € Ø‘˜1˜q™5Õ!Ð!r7   c                óž   € \        R R\        P                  ) \        P                  3R4      p\        RR^ \        P                  3R4      pW.# )rH  Fr™   r4  rj   )rD   r	  r¤  s   &  r5   rm   Úgeninvgauss_gen._shape_infoE  ó@   € Ü˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆÜ˜˜U Q¬¯© K°Ó@ˆØˆxˆr7   c                óþ   € R  p\         P                  ! V\         P                  .R7      pV! WV4      p\         P                  ! V4      P	                  4       '       d    Rp\
        P                  ! V\        ^R7       V# )c                 ó0   € \         P                  ! WV4      # rO   )r   Úgeninvgauss_logpdf©rt   rH  r™   s   &&&r5   Úlogpdf_singleÚ.geninvgauss_gen._logpdf.<locals>.logpdf_singleN  s   € Ü×,Ò,¨Q°1Ó5Ð5r7   r  zjInfinite values encountered in scipy.special.kve(p, b). Values replaced by NaN to avoid incorrect results.r³  )rQ   r  r   r-  ræ  rµ  r¶  r·  )rD   rt   rH  r™   r·  rÓ  rZ   s   &&&&   r5   rý   Úgeninvgauss_gen._logpdfJ  s]   € ò	6ô Ÿš ]¼B¿J¹J¸<ÔHˆá˜! Ó"ˆÜ�8Š8�A‹;�?‰?×ÒðHˆCä�MŠM˜#œ~¸!Õ<Øˆr7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  ©rD   rt   rH  r™   s   &&&&r5   ru   Úgeninvgauss_gen._pdfZ  r0  r7   c                ó˜   a€ V P                  W#4      w  opV3R  lp\        P                  ! V\        P                  .R7      pV! WV4      # )c                 ó   <€ \         P                  ! W.\        4      P                  P	                  \        P
                  4      p\        P                  ! \        R V4      p\        P                  ! VSV 4      ^ ,          # )Ú_geninvgauss_pdf)rQ   r&  r  r'  r(  r)  r   r*  r   r   r,  )rt   rH  r™   r/  r0  r   s   &&&  €r5   Ú_cdf_singleÚ)geninvgauss_gen._cdf.<locals>._cdf_singlea  s\   ø€ ÜŸš ! ¬Ó/×6Ñ6×>Ñ>¼v¿¹ÓOˆIÜ"×.Ò.¬vÐ7IØ/8ó:ˆCô —>’> # r¨1Ó-¨aÕ0Ð0r7   r  )r¥   rQ   r  r   )rD   rt   rH  r™   r  rÀ  r   s   &&&&  @r5   ry   Úgeninvgauss_gen._cdf^  sA   ø€ Ø×"Ñ" 1Ó(‰ˆˆBõ	1ô —l’l ;¼¿
¹
°|ÔDˆá˜1 Ó#Ð#r7   c                ó`   € \         P                  ! V^ 8„  WV3R \        P                  ) R7      # )r   c                 óŽ   € V^,
          \         P                  ! V 4      ,          W ^V ,          ,           ,          ^,          ,
          # r_   rc  r¶  s   &&&r5   r  Ú.geninvgauss_gen._logquasipdf.<locals>.<lambda>o  s(   € °°Aµ´r·v²v¸a³yÕ/@À1È!ÈAÍ#ÅgÅ;ÈqÅ=Ö/Pr7   r  rU  r»  s   &&&&r5   Ú_logquasipdfÚgeninvgauss_gen._logquasipdfl  s+   € ä�Š˜q 1™u q¨Q iÙPÜ+-¯6©6¨'ô3ð 	3r7   Nc                óæ  a	a
€ \         P                  ! V4      '       d1   \         P                  ! V4      '       d   V P                  WW44      pEM‹VP                  ^8X  dC   VP                  ^8X  d2   V P                  VP	                  4       VP	                  4       W44      pEM8\         P
                  ! W4      w  r\        VP                  V4      w  po	\        \         P                  ! V4      4      p\         P                  ! V4      p\         P                  ! W.R.R.R..R7      o
S
P                  '       g¢   \        ;QJ d,    . V	V
3R l\        \        V4      ) ^ 4       4       F  NK  	  5M%! V	V
3R l\        \        V4      ) ^ 4       4       4      pV P                  S
^ ,          S
^,          VV4      P!                  V4      WX&   S
P#                  4        K³  VR8X  d   VP	                  4       pV# )rM   Úmulti_indexÚreadonly©ÚflagsÚop_flagsc              3   ó~   <"  € T F2  pSV,          '       g   SP                   V,          M
\        R 4      x € K4  	  R # 5irO   ©rÉ  Úslice©rB  r  ÚbcÚits   & €€r5   rD  Ú'geninvgauss_gen._rvs.<locals>.<genexpr>Ÿ  ó2   øé € ð ;Ù%9 ð 79¸·e´e˜RŸ^™^¨AÖ.ÄÀtÃÔLÛ%9ùó   ƒ=—&=r‹   )rQ   rG  Ú_rvs_scalarrô   r²  rE  r   rG  r+  rQ  ÚemptyÚnditerÚfinishedÚtuplerR  rç  r°  Úiternext)rD   rH  r™   rô   rõ   rJ  ÚshpÚ
numsamplesÚidxrÒ  rÓ  s   &&&&&    @@r5   rö   Úgeninvgauss_gen._rvsr  sv  ù€ ô �;Š;�q�>Š>œbŸkšk¨!ŸnšnØ×"Ñ" 1¨Ó<ŠCØ�V‰V�qŒ[˜QŸV™V qœ[Ø×"Ñ" 1§6¡6£8¨Q¯V©V«X°tÓJŠCô ×&Ò& qÓ,‰DˆAô # 1§7¡7¨DÓ1‰GˆC�ô œRŸWšW S›\Ó*ˆJô —(’(˜4“.ˆCä—’˜A˜6Ø"/ Ø&0 \°J°<Ð$@ôBˆBð —k—k�k÷ ”eõ ;Ü%*¬C°«I¨:°qÔ%9ó;—e‘eõ ;Ü%*¬C°«I¨:°qÔ%9ó;ó ;�à×+Ñ+¨B¨q­E°2°aµ5¸*Ø,8ó:ß:A¹'À#»,ð ‘à—‘–à�2Œ:Ø—(‘(“*ˆCØˆ
r7   c           	     ó¬  a aaa3€ R pV'       g   ^pS^ 8  d   S) oRpS P                  SS4      pRpS^8¼  g   S^8”  d   RpM?S\        R^\        P                  ! ^S,
          4      ,          ^,          4      8¼  d   R pMR p\	        \        P
                  ! V4      4      p	\        P                  ! V	4      p
\        P                  ! V
4      p^ pV'       Ed   X'       Ed$   RS^,           ,          S,          V,
          p^V,          S^,
          ,          S,          ^,
          pWí^,          ^,          ,
          p^V^,          ,          ^,          WÞ,          ^,          ,
          V,           p\        P                  ! V) \        P                  ! RV^,          ,          4      ,          ^,          4      p\        P                  ! RV,          ^,          4      ) pV\        P                  ! V^,          \        P                  ^,          ,           4      ,          V^,          ,
          pV) \        P                  ! V^,          4      ,          V^,          ,
          pS P                  VSS4      o3S P                  VSS4      S3,
          pS P                  VSS4      S3,
          pVV,
          \        P                  ! RV,          4      ,          pVV,
          \        P                  ! RV,          4      ,          p^pVV3VV 3R lpTpM¶\        P                  ! RS P                  VSS4      ,          4      p^S,           \        P                  ! ^S,           ^,          S^,          ,           4      ,           S,          p^ pV\        P                  ! RS P                  VSS4      ,          4      ,          p^ pVVV 3R lpVV8¼  d   \        R4      hV^ 8:  d   \        R4      h^pWÊ8  dñ   W¬,
          pVVP                  VR7      ,          pVP                  VR7      p VVV,
          V ,          ,           p V V,          V,           p!^\        P                  ! V4      ,          V! V!4      8*  p"\        P                   ! V"4      p#V#^ 8”  d   V!V",          W¼VV#,           % VV#,          pV^ 8X  d'   VV
,          R8¼  d   R	VV
,           R
2p$\#        V$4      hV^,          pKö  EMÖS^S,
          ,          p%\        P$                  ! V%^S,          34      p&\        P                  ! S P                  VSS4      4      p'V'V%,          p(V%^S,          8  dx   \        P                  ! S) 4      p)S^ 8”  d.   V)^S,          S,          V%S,          ,
          ,          S,          p*M0V)\        P                  ! ^S^,          ,          4      ,          p*M^ ^ p*p)V&S^,
          ,          p+^V+,          \        P                  ! V&) S,          ^,          4      ,          S,          p,V(V*,           V,,           p-WÊ8  EdŽ   W¬,
          p\        P                  ! V4      \        P                  ! V4      p!p.VP                  VR7      pV-VP                  VR7      ,          p V V(8*  p/\        P&                  ! V/4      V V(V*,           8*  ,          p0\        P&                  ! V/V0,          4      p1V%V V/,          ,          V(,          V!V/&   V'V.V/&   S^ 8”  d?   V%S,          V V0,          V(,
          S,          V),          ,           ^S,          ,          V!V0&   MIS\        P                  ! V V0,          V(,
          \        P                  ! S4      ,          4      ,          V!V0&   V)V!V0,          S^,
          ,          ,          V.V0&   \        P                  ! V&) S,          ^,          4      SV V1,          V(,
          V*,
          ,          ^V+,          ,          ,
          p2RS,          \        P                  ! V24      ,          V!V1&   V+\        P                  ! V!V1,          ) S,          ^,          4      ,          V.V1&   \        P                  ! VV.,          4      S P                  V!SS4      8*  p"\!        V"4      p#V#^ 8”  g   EKv  V!V",          W¼VV#,           % VV#,          pEK”  \        P(                  ! W¹4      p!V'       d
   ^V!,          p!V!# )FTr£   c                 ó8   <€ SP                  V SS4      S,
          # rO   ©rÆ  )rt   r™   ÚlmrH  rD   s   &€€€€r5   ÚlogqpdfÚ,geninvgauss_gen._rvs_scalar.<locals>.logqpdfâ  s   ø€ Ø×,Ñ,¨Q°°1Ó5¸Õ:Ð:r7   c                 ó*   <€ SP                  V SS4      # rO   rã  )rt   r™   rH  rD   s   &€€€r5   rå  ræ  ð  s   ø€ Ø×,Ñ,¨Q°°1Ó5Ð5r7   zvmin must be smaller than vmax.zumax must be positive.r³  iPÃ  z2Not a single random variate could be generated in zH attempts. Sampling does not appear to work for the provided parameters.r<  iåÿÿÿr`  )Ú_moderR  rQ   r'  rÛ  Ú
atleast_1drQ  ÚzerosÚarccosrQ  r  rÆ  rÓ   r"  r´  r  rè  rz  r.  Úlogical_notr°  )4rD   rH  r™   rÞ  rõ   Ú
invert_resrì  Ú
ratio_unifÚ
mode_shiftÚsize1dÚNrt   Ú	simulatedÚa2Úa1Úp1Úq1Úphir–  Úroot1Úroot2Úd1Úd2ÚvminÚvmaxÚumaxrå  r\  ÚxplusrS  rk  rµ  r  r)  ÚacceptÚ
num_acceptrZ   r|  ÚxsÚk1ÚA1Úk2ÚA2Úk3ÚA3rè  r‰  Úcond1Úcond2Úcond3rÓ  rä  s4   fff&&                                              @r5   r×  Úgeninvgauss_gen._rvs_scalar©  sÞ  û€ ð ˆ
ßØˆJØˆqŒ5à�ˆAØˆJØ�J‰J�q˜!Óˆð ˆ
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Ø¤§¢¨¨E­
 {°Q¥¸Õ':Ó ;Õ;��%‘äŸ&š&  Q¥›-¨4×+<Ñ+<¸SÀ!ÀQÓ+GÑG�Ü  ›[�
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r7   c                ó,  € V^8  dH   V\         P                  ! V^,
          ^,          V^,          ,           4      ^,           V,
          ,          # \         P                  ! ^V,
          ^,          V^,          ,           4      ^V,
          ,
          V,          # r_   rÇ  r®  s   &&&r5   rè  Úgeninvgauss_gen._modeB  sf   € àˆqŒ5ØœŸš  Q¥¨¥
¨Q°­TÕ 1Ó2°QÕ6¸Õ:Õ;Ð;ä—G’G˜Q �U Q�J¨¨A­Õ-Ó.°!°aµ%Õ8¸AÕ=Ð=r7   c                óê  € \         P                  ! W!,           V4      p\         P                  ! W#4      p\        P                  ! V4      \        P                  ! V4      ,          pVP	                  4       '       dq   R p\
        P                  ! V\        ^R7       \        P                  ! V\        P                  \        P                  R7      pWF( ,          WV( ,          ,          W†( &   V# WE,          pV# )z…Infinite values encountered in the moment calculation involving scipy.special.kve. Values replaced by NaN to avoid incorrect results.r³  ©Údtype)r|   ÚkverQ   rW   ræ  rµ  r¶  r·  Ú	full_likerF  r   )	rD   rc   rH  r™   rK  ÚdenomÚinf_valsrZ   rì  s	   &&&&     r5   r,  Úgeninvgauss_gen._munpI  s¥   € Ü�fŠf�Q•U˜AÓˆÜ—’�q“ˆÜ—8’8˜C“=¤2§8¢8¨E£?Õ2ˆØ�<‰<�>Š>ð.ˆCô �MŠM˜#œ~¸!Õ<Ü—’˜S¤"§&¡&´·
±
Ô;ˆAØ˜y�>¨E°)Õ,<Õ<ˆAˆi‰Lð ˆð •ˆAØˆr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rd   rm   rý   ru   ry   rÆ  rö   r×  rè  r,  r‘   r’   r“   s   @r5   r¬  r¬    sE   ø‡ € ñ#òH"òò
ò -ò$ò3ô5ònWòr>÷ð r7   r¬  r<  c                   ó|   a a€ ] tR tRt oRt]P                  tR tR t	V 3R lt
R tR tR tRR	 ltR
 tRtVtV ;t# )Únorminvgauss_geni\  a’  A Normal Inverse Gaussian continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `norminvgauss` is:

.. math::

    f(x, a, b) = \frac{a \, K_1(a \sqrt{1 + x^2})}{\pi \sqrt{1 + x^2}} \,
                 \exp(\sqrt{a^2 - b^2} + b x)

where :math:`x` is a real number, the parameter :math:`a` is the tail
heaviness and :math:`b` is the asymmetry parameter satisfying
:math:`a > 0` and :math:`|b| <= a`.
:math:`K_1` is the modified Bessel function of second kind
(`scipy.special.k1`).

%(after_notes)s

A normal inverse Gaussian random variable `Y` with parameters `a` and `b`
can be expressed as a normal mean-variance mixture:
``Y = b * V + sqrt(V) * X`` where `X` is ``norm(0,1)`` and `V` is
``invgauss(mu=1/sqrt(a**2 - b**2))``. This representation is used
to generate random variates.

Another common parametrization of the distribution (see Equation 2.1 in
[2]_) is given by the following expression of the pdf:

.. math::

    g(x, \alpha, \beta, \delta, \mu) =
    \frac{\alpha\delta K_1\left(\alpha\sqrt{\delta^2 + (x - \mu)^2}\right)}
    {\pi \sqrt{\delta^2 + (x - \mu)^2}} \,
    e^{\delta \sqrt{\alpha^2 - \beta^2} + \beta (x - \mu)}

In SciPy, this corresponds to
:math:`a=\alpha \delta, b=\beta \delta, \text{loc}=\mu, \text{scale}=\delta`.

References
----------
.. [1] O. Barndorff-Nielsen, "Hyperbolic Distributions and Distributions on
       Hyperbolae", Scandinavian Journal of Statistics, Vol. 5(3),
       pp. 151-157, 1978.

.. [2] O. Barndorff-Nielsen, "Normal Inverse Gaussian Distributions and
       Stochastic Volatility Modelling", Scandinavian Journal of
       Statistics, Vol. 24, pp. 1-13, 1997.

%(example)s

c                óH   € V^ 8„  \         P                  ! V4      V8  ,          # r  )rQ   Úabsolute©rD   r˜   r™   s   &&&r5   rd   Únorminvgauss_gen._argcheck”  s   € Ø�A‘œ"Ÿ+š+ a›.¨1Ñ,Õ-Ð-r7   c                óž   € \        R R^ \        P                  3R4      p\        RR\        P                  ) \        P                  3R4      pW.# r¡  rj   r¢  s   &  r5   rm   Únorminvgauss_gen._shape_info—  rÉ  r7   c                ó&   <€ \         SV `  VRR7      # )rM   r…  ©rM   r£   ra  rb  s   &&€r5   r×  Únorminvgauss_gen._fitstartœ  s   ø€ ô ‰wÑ  ¨HÐ Ó5Ð5r7   c                ór  € \         P                  ! V^,          V^,          ,
          4      pV\         P                  ,          p\         P                  ! ^V4      pV\        P
                  ! W&,          4      ,          \         P                  ! W1,          W&,          ,
          V,           4      ,          V,          # rD  )rQ   r'  r  Úhypotr|   Úk1erÓ   )rD   rt   r˜   r™   r(  Úfac1Úsqs   &&&&   r5   ru   Únorminvgauss_gen._pdf¡  sm   € Ü—’˜˜1�˜q !�t�Ó$ˆØ”2—5‘5�yˆÜ�XŠX�a˜‹^ˆØ”b—f’f˜Q�V“nÕ$¤r§v¢v¨a­c°AµD­j¸5Õ.@Ó'AÕAÀBÕFÐFr7   c           
     óô  € \         P                  ! V4      '       d;   \        P                  ! V P                  V\         P
                  W#3R 7      ^ ,          # \         P                  ! V4      p\         P                  ! V4      p. p\        WV4       FO  w  rVpVP                  \        P                  ! V P                  V\         P
                  Wg3R 7      ^ ,          4       KQ  	  \         P                  ! V4      # ©r…  )
rQ   rG  r   r,  ru   rk   ré  rô  Úappendr&  )rD   rt   r˜   r™   Úresultr|  Úa0rC  s   &&&&    r5   r~   Únorminvgauss_gen._sf§  s¬   € Ü�;Š;�q�>Š>ä—>’> $§)¡)¨Q´·±¸a¸VÔDÀQÕGÐGä—’˜aÓ ˆAÜ—’˜aÓ ˆAØˆFÜ # A¨!¦‘�˜Ø—‘œiŸnšn¨T¯Y©Y¸¼B¿F¹FØ35°(ô<Ø<=õ?ö @ñ !-ô —8’8˜FÓ#Ð#r7   c                óæ   a € V 3R  lp\         P                  ! V4      '       d
   V! WV4      # . p\        WV4       F  w  rgpVP                  V! WgV4      4       K   	  \         P                  ! V4      # )c                 óh  <€ V
3R  lpS
P                  W4      pV! WAW 4      pV^ 8X  d   V# V^ 8”  d/   ^pTpWF,           pV! W�W 4      ^ 8”  d   ^V,          pWF,           pK!  M-^pTpWF,
          pV! WqW 4      ^ 8  d   ^V,          pWF,
          pK!  \        P                  ! W7W�W 3S
P                  R7      p	V	# )c                 ó6   <€ SP                  WV4      V,
          # rO   ©r~   )rt   r˜   r™   rƒ   rD   s   &&&&€r5   ÚeqÚ6norminvgauss_gen._isf.<locals>._isf_scalar.<locals>.eq·  s   ø€ à—x‘x  aÓ(¨1Õ,Ð,r7   )rF   rx  )r&  r   r©  rx  )rƒ   r˜   r™   r2	  ÚxmÚemÚdeltaÚleftÚrightr+	  rD   s   &&&       €r5   Ú_isf_scalarÚ*norminvgauss_gen._isf.<locals>._isf_scalarµ  s¾   ø€ õ-ð —‘˜1“ˆBÙ�B˜1“ˆBØ�QŒwà�	Ø�AŒvØ�Ø�Ø�
�Ù˜ 1Ó(¨1Ô,Ø˜e�G�EØ�J’Eð -ð
 �Ø�Ø•z�Ù˜ !Ó'¨!Ô+Ø˜e�G�EØ�:’DÜ—_’_ R¨u¸q¸9Ø*.¯)©)ô5ˆFàˆMr7   )rQ   rG  rô  r*	  r&  )	rD   rƒ   r˜   r™   r9	  r+	  Úq0r,	  rC  s	   f&&&     r5   rˆ   Únorminvgauss_gen._isf´  s`   ø€ õ	ôB �;Š;�q�>Š>Ù˜q QÓ'Ð'àˆFÜ # A¨!¦‘�˜Ø—‘™k¨"°"Ó5Ö6ñ !-ä—8’8˜FÓ#Ð#r7   c                ó  € \         P                  ! V^,          V^,          ,
          4      p\        P                  ^V,          W4R7      pW&,          \         P                  ! V4      \        P                  VVR7      ,          ,           # )rÑ   )ry  rô   rõ   r'  )rQ   r'  r¤  r)  r/  )rD   r˜   r™   rô   rõ   r(  Úigs   &&&&&  r5   rö   Únorminvgauss_gen._rvsÞ  sk   € ô —’˜˜1�˜q !�t�Ó$ˆÜ�\‰\˜Q˜u�W¨4ˆ\ÓKˆØ�vœŸš ›¤d§h¡h°DØ<Hð '/ó 'Jõ Jõ Jð 	Jr7   c                óZ  € \         P                  ! V^,          V^,          ,
          4      pW#,          pV^,          V^,          ,          pRV,          V\         P                  ! V4      ,          ,          pR^^V^,          ,          V^,          ,          ,           ,          V,          pWEWg3# )rÑ   r£  rÇ  )rD   r˜   r™   r(  r&  ÚvarianceÚskewnessÚkurtosiss   &&&     r5   r   Únorminvgauss_gen._statsæ  s~   € Ü—’˜˜1�˜q !�t�Ó$ˆØ�yˆØ�a•4˜% �(•?ˆØ˜•7˜a¤"§'¢'¨%£.Õ0Õ1ˆØ˜!˜a ! Q¥$�h¨¨A­�oÕ-Õ.°Õ6ˆØ˜xÐ1Ð1r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rd   rm   r×  ru   r~   rˆ   rö   r   r‘   r’   r  r   s   @@r5   r	  r	  \  sH   ù‡ € ñ4ðj "×4Ñ4€Mò.òõ
6ò
Gò$ò($ôTJ÷2ò 2r7   r	  Únorminvgaussc                   ó‚   a a€ ] tR tRt oRt]P                  tR tR t	R t
R tR tR tR	 tR
 tRV 3R lltRtVtV ;t# )Úinvweibull_geniò  uD  An inverted Weibull continuous random variable.

This distribution is also known as the FrÃ©chet distribution or the
type II extreme value distribution.

%(before_notes)s

Notes
-----
The probability density function for `invweibull` is:

.. math::

    f(x, c) = c x^{-c-1} \exp(-x^{-c})

for :math:`x > 0`, :math:`c > 0`.

`invweibull` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

References
----------
F.R.S. de Gusmao, E.M.M Ortega and G.M. Cordeiro, "The generalized inverse
Weibull distribution", Stat. Papers, vol. 52, pp. 591-619, 2011.

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úinvweibull_gen._shape_info  r6  r7   c                ó¸   € \         P                  ! W) R ,
          4      p\         P                  ! W) 4      p\         P                  ! V) 4      pW#,          V,          # r8  ©rQ   rU  rÓ   )rD   rt   r\  Úxc1Úxc2s   &&&  r5   ru   Úinvweibull_gen._pdf  s@   € ä�hŠh�q˜"˜s�(Ó#ˆÜ�hŠh�q˜"‹oˆÜ�fŠf�c�T‹lˆØ�w˜�}Ðr7   c                ó^   € \         P                  ! W) 4      p\         P                  ! V) 4      # rO   rK	  )rD   rt   r\  rL	  s   &&& r5   ry   Úinvweibull_gen._cdf  s!   € Ü�hŠh�q˜"‹oˆÜ�vŠv�s�d‹|Ðr7   c                ó@   € \         P                  ! W) ,          ) 4      ) # rO   )rQ   rf  r`  s   &&&r5   r~   Úinvweibull_gen._sf   s   € Ü—’˜!˜R�%˜Ó Ð Ð r7   c                óh   € \         P                  ! \         P                  ! V4      ) RV,          4      # rš  )rQ   rU  r  rg  s   &&&r5   r„   Úinvweibull_gen._ppf#  s!   € Ü�xŠxœŸš ›˜
 D¨¥FÓ+Ð+r7   c                óN   € \         P                  ! V) 4      ) RV,          ,          # rÓ  r—  re  s   &&&r5   rˆ   Úinvweibull_gen._isf&  s   € Ü—’˜1˜"“�  A¥Õ&Ð&r7   c                óH   € \         P                  ! ^W,          ,
          4      # r_   r'  rô  s   &&&r5   r,  Úinvweibull_gen._munp)  s   € Ü�xŠx˜˜A�E�	Ó"Ð"r7   c                óv   € ^\         ,           \         V,          ,           \        P                  ! V4      ,
          # r_   rA  r÷  s   &&r5   r  Úinvweibull_gen._entropy,  s"   € Ø”�xœ& 1�*Õ$¤r§v¢v¨a£yÕ0Ð0r7   c                ó4   <€ Vf   RMTp\         SV `  WR7      # )Nr…  rr  ra  ©rD   rE   rF   rØ  s   &&&€r5   r×  Úinvweibull_gen._fitstart/  s!   ø€ àš‰v¨4ˆÜ‰wÑ  Ð Ó1Ð1r7   r‹   rO   )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   ru   ry   r~   r„   rˆ   r,  r  r×  r‘   r’   r  r   s   @@r5   rG	  rG	  ò  sJ   ù‡ € ñð: "×4Ñ4€MòEòòò!ò,ò'ò#ò1÷2÷ 2r7   rG	  Ú
invweibullc                   óR   a € ] tR tRt o RtR tR tRR ltR tR t	R	 t
R
 tRtV tR# )Újf_skew_t_geni8  a   Jones and Faddy skew-t distribution.

%(before_notes)s

Notes
-----
The probability density function for `jf_skew_t` is:

.. math::

    f(x; a, b) = C_{a,b}^{-1}
                \left(1+\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{a+1/2}
                \left(1-\frac{x}{\left(a+b+x^2\right)^{1/2}}\right)^{b+1/2}

for real numbers :math:`a>0` and :math:`b>0`, where
:math:`C_{a,b} = 2^{a+b-1}B(a,b)(a+b)^{1/2}`, and :math:`B` denotes the
beta function (`scipy.special.beta`).

When :math:`a<b`, the distribution is negatively skewed, and when
:math:`a>b`, the distribution is positively skewed. If :math:`a=b`, then
we recover the `t` distribution with :math:`2a` degrees of freedom.

`jf_skew_t` takes :math:`a` and :math:`b` as shape parameters.

%(after_notes)s

References
----------
.. [1] M.C. Jones and M.J. Faddy. "A skew extension of the t distribution,
       with applications" *Journal of the Royal Statistical Society*.
       Series B (Statistical Methodology) 65, no. 1 (2003): 159-174.
       :doi:`10.1111/1467-9868.00378`

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# r¡  rj   r¢  s   &  r5   rm   Újf_skew_t_gen._shape_info]  r¦  r7   c                óÜ  € ^W#,           ^,
          ,          \         P                  ! W#4      ,          \        P                  ! W#,           4      ,          p^V\        P                  ! W#,           V^,          ,           4      ,          ,           VR,           ,          p^V\        P                  ! W#,           V^,          ,           4      ,          ,
          VR,           ,          pWV,          V,          # rI  )r|   r©  rQ   r'  )rD   rt   r˜   r™   r\  rú  rû  s   &&&&   r5   ru   Újf_skew_t_gen._pdfb  s�   € Ø�!•%˜!•)ÕœrŸwšw q›}Õ,¬r¯wªw°qµu«~Õ=ˆØ�!”b—g’g˜a�e a¨1¥f�nÓ-Õ-Õ-°1°sµ7Õ;ˆØ�!”b—g’g˜a�e a¨1¥f�nÓ-Õ-Õ-°1°sµ7Õ;ˆØ�w˜�{Ðr7   Nc                óî   € VP                  WV4      p^V,          ^,
          \        P                  ! W,           4      ,          p^\        P                  ! V^V,
          ,          4      ,          pWg,          # rD  )r©  rQ   r'  )rD   r˜   r™   rô   rõ   rú  rû  Úd3s   &&&&&   r5   rö   Újf_skew_t_gen._rvsh  sR   € Ø×Ñ˜q TÓ*ˆØ�"�f�q�jœBŸGšG A¥E›NÕ*ˆØ”—’˜˜q 2�v�Ó'Õ'ˆØ�wˆr7   c                ó®   € ^V\         P                  ! W#,           V^,          ,           4      ,          ,           R,          p\        P                  ! W#V4      # r 	  )rQ   r'  r|   rº  ©rD   rt   r˜   r™   rv  s   &&&& r5   ry   Újf_skew_t_gen._cdfn  s:   € Ø�”R—W’W˜Q�U Q¨!¥V�^Ó,Õ,Õ,°Õ3ˆÜ�zŠz˜! Ó"Ð"r7   c                ó®   € ^V\         P                  ! W#,           V^,          ,           4      ,          ,           R,          p\        P                  ! W#V4      # r 	  )rQ   r'  r|   r½  ri	  s   &&&& r5   r~   Újf_skew_t_gen._sfr  s:   € Ø�”R—W’W˜Q�U Q¨!¥V�^Ó,Õ,Õ,°Õ3ˆÜ�{Š{˜1 Ó#Ð#r7   c                óö   € \         P                  WV4      p^V,          ^,
          \        P                  ! W#,           4      ,          p^\        P                  ! V^V,
          ,          4      ,          pWV,          # rD  )r©  rš  rQ   r'  )rD   rƒ   r˜   r™   rú  rû  rf	  s   &&&&   r5   r„   Újf_skew_t_gen._ppfv  sP   € Ü�X‰X�a˜AÓˆØ�"�f�q�jœBŸGšG A¥E›NÕ*ˆØ”—’˜˜q 2�v�Ó'Õ'ˆØ�wˆr7   c           	     óô   € R pVRV,          8„  VRV,          8„  ,          V^ 8¬  ,          p\         P                  ! VWV3\        P                  ! V\        P                  .R7      \        P
                  R7      # )z…Returns the n-th moment(s) where all the following hold:

- n >= 0
- a > n / 2
- b > n / 2

The result is np.nan in all other cases.
c                óø  € W,           RV ,          ,          p^V ,          \         P                  ! W4      ,          p\        P                  ! V ^,           4      p\        P                  ! V^,          ^ 8„  R^4      p\         P                  ! VRV ,          ,           V,
          VRV ,          ,
          V,           4      p\         P
                  ! W4      V,          V,          pW4,          VP                  4       ,          # )zOComputes E[T^(n_k)] where T is skew-t distributed with
parameters a_k and b_k.
r£   r  )r|   r©  rQ   r¯  r±  rõ  rè  )	Ún_kÚa_kÚb_krK  r	  Úindicesr™  r  Ú	sum_termss	   &&&      r5   Ú
nth_momentÚ'jf_skew_t_gen._munp.<locals>.nth_moment…  s¬   € ð •9 #¨¥)Õ,ˆCØ˜•HœrŸwšw sÓ0Õ0ˆEä—i’i  a¥Ó(ˆGÜ—(’(˜7 Q�;¨™?¨B°Ó2ˆCÜ—’˜˜c C�i�¨'Õ1°3¸¸s½µ?ÀWÕ3LÓMˆAÜŸš Ó-°Õ3°aÕ7ˆIà•; §¡£Õ0Ð0r7   r£   r  r  ©r  r  rQ   r  r   rF  )rD   rc   r˜   r™   rv	  Únth_moment_valids   &&&&  r5   r,  Újf_skew_t_gen._munp|  sc   € ò	1ð   a¥™K¨A°°aµ©KÕ8¸AÀ¹FÕCÐÜ�ŠØØ�1ˆIÜ�LŠL˜¬R¯Z©Z¨LÔ9Ü—v‘vô	
ð 	
r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   ru   rö   ry   r~   r„   r,  r‘   r’   r“   s   @r5   r`	  r`	  8  s3   ø‡ € ñ#òHò
ôò#ò$ò÷
ð 
r7   r`	  Ú	jf_skew_tc                   óf   a € ] tR tRt o Rt]P                  tR tR t	R t
R tR tR tR	 tR
tV tR# )Újohnsonsb_geniŸ  aá  A Johnson SB continuous random variable.

%(before_notes)s

See Also
--------
johnsonsu

Notes
-----
The probability density function for `johnsonsb` is:

.. math::

    f(x, a, b) = \frac{b}{x(1-x)}  \phi(a + b \log \frac{x}{1-x} )

where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`
and :math:`x \in [0,1]`.  :math:`\phi` is the pdf of the normal
distribution.

`johnsonsb` takes :math:`a` and :math:`b` as shape parameters.

%(after_notes)s

%(example)s

c                ó   € V^ 8„  W8H  ,          # r  r‹   r	  s   &&&r5   rd   Újohnsonsb_gen._argcheck½  ó   € Ø�A‘˜!™&Õ!Ð!r7   c                óž   € \        R R\        P                  ) \        P                  3R4      p\        RR^ \        P                  3R4      pW.# r¡  rj   r¢  s   &  r5   rm   Újohnsonsb_gen._shape_infoÀ  r²  r7   c                ó¤   € \        W#\        P                  ! V4      ,          ,           4      pVR ,          V^V,
          ,          ,          V,          # r8  )rÖ   r|   rü  )rD   rt   r˜   r™   Útrms   &&&& r5   ru   Újohnsonsb_gen._pdfÅ  s6   € ä˜œbŸhšh q›k�MÕ)Ó*ˆØ��u�a˜˜1�•g�˜sÕ"Ð"r7   c                óZ   € \        W#\        P                  ! V4      ,          ,           4      # rO   )rÜ   r|   rü  r°  s   &&&&r5   ry   Újohnsonsb_gen._cdfÊ  s   € Ü˜œrŸxšx¨›{�]Õ*Ó+Ð+r7   c                ój   € \         P                  ! R V,          \        V4      V,
          ,          4      # r8  )r|   r÷  rã   rÄ  s   &&&&r5   r„   Újohnsonsb_gen._ppfÍ  ó#   € Ü�xŠx˜˜a�¤9¨Q£<°!Õ#3Õ4Ó5Ð5r7   c                óZ   € \        W#\        P                  ! V4      ,          ,           4      # rO   )ræ   r|   rü  r°  s   &&&&r5   r~   Újohnsonsb_gen._sfÐ  s   € Ü˜œbŸhšh q›k�MÕ)Ó*Ð*r7   c                ój   € \         P                  ! R V,          \        V4      V,
          ,          4      # r8  )r|   r÷  rì   rÄ  s   &&&&r5   rˆ   Újohnsonsb_gen._isfÓ  rŠ	  r7   r‹   N)rŒ   r�   rŽ   r�   r�   r   rI  rJ  rd   rm   ru   ry   r„   r~   rˆ   r‘   r’   r“   s   @r5   r}	  r}	  Ÿ  s?   ø‡ € ñð6 "×4Ñ4€Mò"òò
#ò
,ò6ò+÷6ð 6r7   r}	  Ú	johnsonsbc                   óX   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tRR
 ltRtV tR# )Újohnsonsu_geniÚ  aÕ  A Johnson SU continuous random variable.

%(before_notes)s

See Also
--------
johnsonsb

Notes
-----
The probability density function for `johnsonsu` is:

.. math::

    f(x, a, b) = \frac{b}{\sqrt{x^2 + 1}}
                 \phi(a + b \log(x + \sqrt{x^2 + 1}))

where :math:`x`, :math:`a`, and :math:`b` are real scalars; :math:`b > 0`.
:math:`\phi` is the pdf of the normal distribution.

`johnsonsu` takes :math:`a` and :math:`b` as shape parameters.

The first four central moments are calculated according to the formulas
in [1]_.

%(after_notes)s

References
----------
.. [1] Taylor Enterprises. "Johnson Family of Distributions".
   https://variation.com/wp-content/distribution_analyzer_help/hs126.htm

%(example)s

c                ó   € V^ 8„  W8H  ,          # r  r‹   r	  s   &&&r5   rd   Újohnsonsu_gen._argcheckþ  r€	  r7   c                óž   € \        R R\        P                  ) \        P                  3R4      p\        RR^ \        P                  3R4      pW.# r¡  rj   r¢  s   &  r5   rm   Újohnsonsu_gen._shape_info  r²  r7   c                óÎ   € W,          p\        W#\        P                  ! V4      ,          ,           4      pVR ,          \        P                  ! VR ,           4      ,          V,          # r8  )rÖ   rQ   Úarcsinhr'  )rD   rt   r˜   r™   rî  r„	  s   &&&&  r5   ru   Újohnsonsu_gen._pdf  sE   € ð �SˆÜ˜¤§
¢
¨1£Õ-Õ-Ó.ˆØ��u”R—W’W˜R �V“_Õ$ SÕ(Ð(r7   c                óZ   € \        W#\        P                  ! V4      ,          ,           4      # rO   )rÜ   rQ   r—	  r°  s   &&&&r5   ry   Újohnsonsu_gen._cdf  s   € Ü˜¤§¢¨A£Õ.Õ.Ó/Ð/r7   c                ó\   € \         P                  ! \        V4      V,
          V,          4      # rO   )rQ   Úsinhrã   rÄ  s   &&&&r5   r„   Újohnsonsu_gen._ppf  ó   € Ü�wŠwœ	 !› qÕ(¨AÕ-Ó.Ð.r7   c                óZ   € \        W#\        P                  ! V4      ,          ,           4      # rO   )ræ   rQ   r—	  r°  s   &&&&r5   r~   Újohnsonsu_gen._sf  s   € Ü˜¤§
¢
¨1£Õ-Õ-Ó.Ð.r7   c                ó\   € \         P                  ! \        V4      V,
          V,          4      # rO   )rQ   rœ	  rì   r°  s   &&&&r5   rˆ   Újohnsonsu_gen._isf  rž	  r7   c                ó\  € Rw  rErgVR,          p\         P                  ! V4      p	W,          p
RV9   d&   V	R,          ) \         P                  ! V
4      ,          pRV9   dN   R\        P                  ! V4      ,          V	\         P
                  ! ^V
,          4      ,          ^,           ,          pRV9   dÞ   V	R,          \        P                  ! V4      R,          ,          p^\         P                  ! V
4      ,          pW™^,           ,          \         P                  ! ^V
,          4      ,          p\         P                  ! ^4      ^V	\         P
                  ! ^V
,          4      ,          ,           R,          ,          pV) WÍ,           ,          V,          pRV9   Ed   ^^V	,          ,           p^V	^,          ,          V	^,           ,          \         P
                  ! ^V
,          4      ,          pV	^,          \         P
                  ! ^V
,          4      ,          pR	^V	^,          ,          ,           ^V	^,          ,          ,           V	^,          ,           p^^V	\         P
                  ! ^V
,          4      ,          ,           ^,          ,          pW¼,           Wß,          ,           V,          ^,
          pWEWg3# )
Nrì  r£   r  rj  rk  rï  rö  rS  r_  )rQ   rÓ   rœ	  r|   rf  r8  r'  )rD   r˜   r™   rl  ry  rz  r{  r|  Úbn2Úexpbn2Úa_brû  rü  rý  r	  rô  s   &&&&            r5   r   Újohnsonsu_gen._stats  sÏ  € ð 1‰ˆ�à��fˆÜ—’˜“ˆØ�eˆà�'Œ>Ø˜#•+�¤§¢¨£Õ,ˆBØ�'Œ>Ø”b—h’h˜s“mÕ# V¬B¯GªG°A°cµE«NÕ%:¸QÕ%>Õ?ˆCØ�'Œ>Ø˜•œbŸhšh s›m¨SÕ0Õ0ˆBØ”2—7’7˜3“<•ˆBØ A�:Õ&¬¯ª°°3µ«Õ7ˆBÜ—G’G˜A“J ! f¬r¯wªw°q¸µu«~Õ&=Õ"=ÀÕ!EÕEˆEØ�˜�• 5Õ(ˆBØ�'�>Ø�Q�v•X•ˆBØ�6˜1•9• ¨¥
Õ+¬b¯gªg°a¸µe«nÕ<ˆBØ˜•œRŸWšW Q s¥U›^Õ+ˆBØ�a˜ �	•kÕ! A f¨a¥i¥KÕ/°&¸!µ)Õ;ˆBØ�q˜6¤"§'¢'¨!¨C­%£.Õ0Õ0°1Õ4Õ4ˆEØ•'˜B�E•/ UÕ*¨QÕ.ˆBØ˜ˆÐr7   r‹   Nrq  )rŒ   r�   rŽ   r�   r�   rd   rm   ru   ry   r„   r~   rˆ   r   r‘   r’   r“   s   @r5   r‘	  r‘	  Ú  s8   ø‡ € ñ"òF"òò
)ò0ò/ò/ò/÷ò r7   r‘	  Ú	johnsonsuc                   ón   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tRR ltRR ltRtV tR# )Ú
landau_geni:  a¸  A Landau continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `landau` ([1]_, [2]_) is:

.. math::

    f(x) = \frac{1}{\pi}\int_0^\infty \exp(-t \log t - xt)\sin(\pi t) dt

for a real number :math:`x`.

%(after_notes)s

Often (e.g. [2]_), the Landau distribution is parameterized in terms of a
location parameter :math:`\mu` and scale parameter :math:`c`, the latter of
which *also* introduces a location shift. If ``mu`` and ``c`` are used to
represent these parameters, this corresponds with SciPy's parameterization
with ``loc = mu + 2*c / np.pi * np.log(c)`` and ``scale = c``.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
methods. [1]_

References
----------
.. [1] Landau, L. (1944). "On the energy loss of fast particles by
       ionization". J. Phys. (USSR). 8: 201.
.. [2] "Landau Distribution", Wikipedia,
       https://en.wikipedia.org/wiki/Landau_distribution
.. [3] Chambers, J. M., Mallows, C. L., & Stuck, B. (1976).
       "A method for simulating stable random variables."
       Journal of the American Statistical Association, 71(354), 340-344.
.. [4] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.
.. [5] Yoshimura, T. "Numerical Evaluation and High Precision Approximation
       Formula for Landau Distribution".
       :doi:`10.36227/techrxiv.171822215.53612870/v2`

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úlandau_gen._shape_infof  r¼   r7   c                ó   € R # )gÚïXÐ(û@r‹   rl   s   &r5   r  Úlandau_gen._entropyi  s   € á"r7   c                ó2   € \         P                  ! V^ ^4      # r  )rq   Ú_landau_pdfr¿   s   &&r5   ru   Úlandau_gen._pdfm  r  r7   c                ó2   € \         P                  ! V^ ^4      # r  )rq   Ú_landau_cdfr¿   s   &&r5   ry   Úlandau_gen._cdfp  r  r7   c                ó2   € \         P                  ! V^ ^4      # r  )rq   Ú
_landau_sfr¿   s   &&r5   r~   Úlandau_gen._sfs  s   € Ü�~Š~˜a  AÓ&Ð&r7   c                ó2   € \         P                  ! V^ ^4      # r  )rq   Ú_landau_ppfr¢  s   &&r5   r„   Úlandau_gen._ppfv  r  r7   c                ó2   € \         P                  ! V^ ^4      # r  )rq   Ú_landau_isfr¢  s   &&r5   rˆ   Úlandau_gen._isfy  r  r7   c                ó~   € \         P                  \         P                  \         P                  \         P                  3# rO   r  rl   s   &r5   r   Úlandau_gen._stats|  r  r7   c                ó4   € V^ 8”  d   \         P                  # ^# r  r  rb   s   &&r5   r,  Úlandau_gen._munp  s   € Ø˜QœŒr�v‰vÐ% AÐ%r7   Nc                ó¨   € \        V\        4      '       d   VP                  4       p\        P                  ! V. RO4      w  r4pWEV,
          ^,          3# r!  r&  r(  s   &&&   r5   r×  Úlandau_gen._fitstart‚  r-  r7   c                óæ  € \         P                  ^,          pVP                  \         P                  ) ^,          \         P                  ^,          VR7      pVP                  VR7      p^\         P                  ,          W4,           \         P                  ! V4      ,          \         P
                  ! W5,          \         P                  ! V4      ,          W4,           ,          4      ,
          ,          pV# )rÑ   r³  )rQ   r  r´  râ  rÉ  r  rQ  )rD   rô   rõ   Úpi_2ÚUÚWÚSs   &&&    r5   rö   Úlandau_gen._rvs‰  sœ   € ä�u‰u�q�yˆØ× Ñ ¤"§%¡% ¨!¥¬R¯U©U°Q­Y¸TÐ ÓBˆØ×-Ñ-°4Ð-Ó8ˆØ”—‘�I˜$�(¤b§f¢f¨Q£iÕ/ÜŸ6š6 4¥8¬b¯fªf°Q«iÕ#7¸D½HÕ"EÓFõGõ Hˆàˆr7   r‹   rO   r.  )rŒ   r�   rŽ   r�   r�   rm   r  ru   ry   r~   r„   rˆ   r   r,  r×  rö   r‘   r’   r“   s   @r5   rª	  rª	  :  sG   ø‡ € ñ*òVò#ò(ò(ò'ò(ò(ò.ò&ô"÷ò r7   rª	  Úlandauc                   óˆ   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR t]]! ]RR7      R 4       4       tRtV tR# )Úlaplace_geni–  zâA Laplace continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `laplace` is

.. math::

    f(x) = \frac{1}{2} \exp(-|x|)

for a real number :math:`x`.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úlaplace_gen._shape_infoª  r¼   r7   Nc                ó*   € VP                  ^ ^VR7      # )r   r³  )Úlaplaceró   s   &&&r5   rö   Úlaplace_gen._rvs­  s   € Ø×#Ñ# A q¨tÐ#Ó4Ð4r7   c                óP   € R \         P                  ! \        V4      ) 4      ,          # r  )rQ   rÓ   r	  r¿   s   &&r5   ru   Úlaplace_gen._pdf°  s   € à”2—6’6œ3˜q›6˜'“?Õ"Ð"r7   c           
     ó0  € \         P                  ! R R7      ;_uu_ 4        \         P                  ! V^ 8„  RR\         P                  ! V) 4      ,          ,
          R\         P                  ! V4      ,          4      uuRRR4       #   + '       g   i     R# ; i)rl  r­  r–   r£   N)rQ   ro  r±  rÓ   r¿   s   &&r5   ry   Úlaplace_gen._cdf´  sS   € Ü�[Š[˜h×'Ö'Ü—8’8˜A ™E 3¨¬R¯VªV°Q°B«Z­Õ#7¸¼R¿VºVÀA»Y½ÓG÷ (×'×'Ó'ús    ABÂB	c                ó&   € V P                  V) 4      # rO   ©ry   r¿   s   &&r5   r~   Úlaplace_gen._sf¸  s   € à�y‰y˜!˜‹}Ðr7   c                ó´   € \         P                  ! VR 8„  \         P                  ! ^^V,
          ,          4      ) \         P                  ! ^V,          4      4      # r  ©rQ   r±  r  rÉ   s   &&r5   r„   Úlaplace_gen._ppf¼  s8   € Ü�xŠx˜˜C™¤"§&¢&¨¨A¨a­C­£/Ð!1´2·6²6¸!¸A½#³;Ó?Ð?r7   c                ó&   € V P                  V4      ) # rO   r´  rÉ   s   &&r5   rˆ   Úlaplace_gen._isf¿  s   € à—	‘	˜!“ˆ}Ðr7   c                ó   € R# )r   )r   rÑ   r   r¦  r‹   rl   s   &r5   r   Úlaplace_gen._statsÃ  s   € ØÐr7   c                ó<   € \         P                  ! ^4      ^,           # rD  rc  rl   s   &r5   r  Úlaplace_gen._entropyÆ  s   € Ü�vŠv�a‹y˜�{Ðr7   zÒ        This function uses explicit formulas for the maximum likelihood
        estimation of the Laplace distribution parameters, so the keyword
        arguments `loc`, `scale`, and `optimizer` are ignored.

r  c                óâ   € \        WW#4      w  rpVf   \        P                  ! V4      pVfA   \        P                  ! \        P                  ! W,
          4      4      \        V4      ,          pWE3# rO   )rR  rQ   Úmedianrè  r	  rç  )rD   rE   rF   r4   r  r  s   &&*,  r5   rB   Úlaplace_gen.fitÉ  s\   € ô 9¸Ø9=óEÑˆ�Fð Š<Ü—9’9˜T“?ˆDàŠ>Ü—f’fœRŸVšV D¥KÓ0Ó1´S¸³YÕ>ˆFàˆ|Ðr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   ry   r~   r„   rˆ   r   r  rK   r
   r   rB   r‘   r’   r“   s   @r5   rÌ	  rÌ	  –  sd   ø‡ € ñò&ô5ò#òHòò@òòòð Ù ð 6Fô Gñó	Gó ö
r7   rÌ	  rÐ	  c                   óZ   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tRtV tR# )Úlaplace_asymmetric_geniá  u}  An asymmetric Laplace continuous random variable.

%(before_notes)s

See Also
--------
laplace : Laplace distribution

Notes
-----
The probability density function for `laplace_asymmetric` is

.. math::

   f(x, \kappa) &= \frac{1}{\kappa+\kappa^{-1}}\exp(-x\kappa),\quad x\ge0\\
                &= \frac{1}{\kappa+\kappa^{-1}}\exp(x/\kappa),\quad x<0\\

for :math:`-\infty < x < \infty`, :math:`\kappa > 0`.

`laplace_asymmetric` takes ``kappa`` as a shape parameter for
:math:`\kappa`. For :math:`\kappa = 1`, it is identical to a
Laplace distribution.

%(after_notes)s

Note that the scale parameter of some references is the reciprocal of
SciPy's ``scale``. For example, :math:`\lambda = 1/2` in the
parameterization of [1]_ is equivalent to ``scale = 2`` with
`laplace_asymmetric`.

References
----------
.. [1] "Asymmetric Laplace distribution", Wikipedia
        https://en.wikipedia.org/wiki/Asymmetric_Laplace_distribution

.. [2] Kozubowski TJ and PodgÃ³rski K. A Multivariate and
       Asymmetric Generalization of Laplace Distribution,
       Computational Statistics 15, 531--540 (2000).
       :doi:`10.1007/PL00022717`

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# )ÚkappaFr4  rj   rl   s   &r5   rm   Ú"laplace_asymmetric_gen._shape_info  s   € Ü˜7 E¨A¬r¯v©v¨;¸ÓGÐHÐHr7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  ©rD   rt   rè	  s   &&&r5   ru   Úlaplace_asymmetric_gen._pdf  s   € Ü�vŠv�d—l‘l 1Ó,Ó-Ð-r7   c                ó¤   € ^V,          pV\         P                  ! V^ 8¬  V) V4      ,          pV\         P                  ! W#,           4      ,          pV# r_   rÚ	  )rD   rt   rè	  Úkapinvr·  s   &&&  r5   rý   Úlaplace_asymmetric_gen._logpdf  sB   € Ø�5•ˆØ”"—(’(˜1 ™6 E 6¨6Ó2Õ2ˆØŒr�vŠv�e•lÓ#Õ#ˆØˆ
r7   c                ó  € ^V,          pW#,           p\         P                  ! V^ 8¬  ^\         P                  ! V) V,          4      W4,          ,          ,
          \         P                  ! W,          4      W$,          ,          4      # r_   ©rQ   r±  rÓ   ©rD   rt   rè	  rî	  Ú
kappkapinvs   &&&  r5   ry   Úlaplace_asymmetric_gen._cdf  s^   € Ø�5•ˆØ•\ˆ
Ü�xŠx˜˜Q™ØœBŸFšF A 2 e¥8Ó,¨fÕ.?Õ@Õ@ÜŸš˜q�xÓ(¨%Õ*:Õ;ó=ð 	=r7   c           	     ó  € ^V,          pW#,           p\         P                  ! V^ 8¬  \         P                  ! V) V,          4      W4,          ,          ^\         P                  ! W,          4      W$,          ,          ,
          4      # r_   rñ	  rò	  s   &&&  r5   r~   Úlaplace_asymmetric_gen._sf   s`   € Ø�5•ˆØ•\ˆ
Ü�xŠx˜˜Q™ÜŸš ˜r %�xÓ(¨&Õ*;Õ<ØœBŸFšF 1¥8Ó,¨eÕ.>Õ?Õ?óAð 	Ar7   c                ó  € ^V,          pW#,           p\         P                  ! WV,          8¬  \         P                  ! ^V,
          V,          V,          4      ) V,          \         P                  ! W,          V,          4      V,          4      # r_   rÚ	  ©rD   rƒ   rè	  rî	  ró	  s   &&&  r5   r„   Úlaplace_asymmetric_gen._ppf'  sg   € Ø�5•ˆØ•\ˆ
Ü�xŠx˜ :Õ-Ñ-ÜŸš  Q¥¨
Õ 2°5Õ 8Ó9Ð9¸&Õ@ÜŸš˜q�|¨EÕ1Ó2°5Õ8ó:ð 	:r7   c                ó  € ^V,          pW#,           p\         P                  ! WV,          8*  \         P                  ! W,          V,          4      ) V,          \         P                  ! ^V,
          V,          V,          4      V,          4      # r_   rÚ	  rø	  s   &&&  r5   rˆ   Úlaplace_asymmetric_gen._isf.  si   € Ø�5•ˆØ•\ˆ
Ü�xŠx˜ JÕ.Ñ.ÜŸš ¥¨UÕ 2Ó3Ð3°FÕ:ÜŸš  A¥ zÕ1°%Õ7Ó8¸Õ>ó@ð 	@r7   c                óÊ  € ^V,          pW!,
          pW",          W,          ,           pR^\         P                  ! V^4      ,
          ,          \         P                  ! ^\         P                  ! V^4      ,           R4      ,          pR^\         P                  ! V^4      ,           ,          \         P                  ! ^\         P                  ! V^4      ,           ^4      ,          pW4WV3# )rM   rÒ   rS  rJ  rÆ  )rD   rè	  rî	  Úmnrê  r{  r|  s   &&     r5   r   Úlaplace_asymmetric_gen._stats5  sž   € Ø�5•ˆØ�^ˆØ�m˜e�kÕ)ˆØ�!”B—H’H˜U AÓ&Õ&Õ'¬¯ª°´2·8²8¸EÀ1Ó3EÕ1EÀsÓ(KÕKˆØ�!”B—H’H˜U AÓ&Õ&Õ'¬¯ª°´2·8²8¸EÀ1Ó3EÕ1EÀqÓ(IÕIˆØ˜ˆÐr7   c                óX   € ^\         P                  ! V^V,          ,           4      ,           # r_   rc  ©rD   rè	  s   &&r5   r  Úlaplace_asymmetric_gen._entropy=  s   € Ø”2—6’6˜%  %¥�-Ó(Õ(Ð(r7   r‹   Nr«  r“   s   @r5   ræ	  ræ	  á  s@   ø‡ € ñ*òVIò.òò=òAò:ò@ò÷)ð )r7   ræ	  Úlaplace_asymmetricc                 ó  € \        V\        4      '       g   \        P                  ! V4      pVP	                  R R4      pVP	                  RR4      pV P
                  '       d%   \        V P
                  P                  R4      4      M^ p. p. pV P
                  '       d›   V P
                  P                  RR4      P                  4       p	\        V	4       Fa  w  r«R\        V
4      ,           pVRV,           RV,           .p\        W=4      pVP                  V4       VP                  V4       Vf   K]  WãV&   Kc  	  0 RmVmp\        V4      P                  V4      pV'       d   \        RV R24      h\        V4      V8”  d   \        R	4      hRWE0Vm9  d   \!        R
4      h\        V\        4      '       d   VP#                  4       MTp\        P$                  ! V4      P'                  4       '       g   \)        R4      hV.VOVNVN5# )r  Nr  Ú,Ú rœ  Úfix_zUnknown keyword arguments: r1   zToo many positional arguments.r   r!  >   r-   r  r.   r  r0   r/   )r>   r)   rQ   r#  r<   Úshapesrç  Úsplitr�  Ú	enumerateÚstrr   r*	  ÚsetÚ
differencer3   rz  rÕ  r$  r%  r"  )ÚdistrE   rF   r4   r  r  Ú
num_shapesÚfshape_keysÚfshapesr
  r  rj  ÚkeyÚnamesr˜  Ú
known_keysÚunknown_keysÚ
uncensoreds   &&&&              r5   rR  rR  D  sÅ  € Ü�dœL×)Ò)Ü�zŠz˜$Óˆà�8‰8�F˜DÓ!€DØ�X‰X�h Ó%€Fà04··°”�T—[‘[×&Ñ& sÓ+Ô,À€JØ€KØ€Gð
 ‡{‡{€{Ø—‘×$Ñ$ S¨#Ó.×4Ñ4Ó6ˆÜ˜fÖ%‰DˆAØœ˜A›•,ˆCØ˜# �' 6¨A¥:Ð.ˆEÜ& tÓ3ˆCØ×Ñ˜sÔ#Ø�N‰N˜3ÔØŒØ�S“	ñ &ò2Ø%0ð2€Jä�t“9×'Ñ'¨
Ó3€LßÜÐ5°l°^À1ÐEÓFÐFä
ˆ4ƒy�:ÔÜÐ8Ó9Ð9à�DÐ+ 7Ð+Ô+ô ð 'ó (ð 	(ô &0°´l×%CÒ%C�—‘Ô!È€JÜ�;Š;�zÓ"×&Ñ&×(Ò(ÜÐ?Ó@Ð@àÐ)�7Ð)˜DÐ) &Ñ)Ð)r7   c                   óf   a € ] tR tRt o Rt]P                  tR tR t	R t
R tR tR tR	 tR
tV tR# )Úlevy_geniu  a§  A Levy continuous random variable.

%(before_notes)s

See Also
--------
levy_stable, levy_l

Notes
-----
The probability density function for `levy` is:

.. math::

    f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp\left(-\frac{1}{2x}\right)

for :math:`x > 0`.

This is the same as the Levy-stable distribution with :math:`a=1/2` and
:math:`b=1`.

%(after_notes)s

Examples
--------
>>> import numpy as np
>>> from scipy.stats import levy
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

>>> mean, var, skew, kurt = levy.stats(moments='mvsk')

Display the probability density function (``pdf``):

>>> # `levy` is very heavy-tailed.
>>> # To show a nice plot, let's cut off the upper 40 percent.
>>> a, b = levy.ppf(0), levy.ppf(0.6)
>>> x = np.linspace(a, b, 100)
>>> ax.plot(x, levy.pdf(x),
...        'r-', lw=5, alpha=0.6, label='levy pdf')

Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = levy()
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = levy.ppf([0.001, 0.5, 0.999])
>>> np.allclose([0.001, 0.5, 0.999], levy.cdf(vals))
True

Generate random numbers:

>>> r = levy.rvs(size=1000)

And compare the histogram:

>>> # manual binning to ignore the tail
>>> bins = np.concatenate((np.linspace(a, b, 20), [np.max(r)]))
>>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úlevy_gen._shape_infoÀ  r¼   r7   c                óÔ   € ^\         P                  ! ^\         P                  ,          V,          4      ,          V,          \         P                  ! R^V,          ,          4      ,          # rÓ  r  r¿   s   &&r5   ru   Úlevy_gen._pdfÃ  s=   € à”2—7’7˜1œRŸU™U�7 1�9Ó%Õ%¨Õ)¬B¯FªF°2°q¸µsµ8Ó,<Õ<Ð<r7   c                ód   € \         P                  ! \        P                  ! R V,          4      4      # r  )r|   ÚerfcrQ   r'  r¿   s   &&r5   ry   Úlevy_gen._cdfÇ  s   € ä�wŠw”r—w’w˜s Q�wÓ'Ó(Ð(r7   c                ód   € \         P                  ! \        P                  ! R V,          4      4      # r  r   r¿   s   &&r5   r~   Úlevy_gen._sfË  s   € Ü�vŠv”b—g’g˜c A�gÓ&Ó'Ð'r7   c                óD   € \        V^,          4      pRW",          ,          # ©rÑ   r–   r  ©rD   rƒ   r˜  s   && r5   r„   Úlevy_gen._ppfÎ  s   € ä˜˜!�‹nˆØ�c•iÕ Ð r7   c                óX   € ^^\         P                  ! V4      ^,          ,          ,          # r_   )r|   Úerfinvr¢  s   &&r5   rˆ   Úlevy_gen._isfÓ  s   € Ø�!”B—I’I˜a“L !•OÕ#Õ$Ð$r7   c                ó~   € \         P                  \         P                  \         P                  \         P                  3# rO   rE  rl   s   &r5   r   Úlevy_gen._statsÖ  r  r7   r‹   N©rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   ru   ry   r~   r„   rˆ   r   r‘   r’   r“   s   @r5   r
  r
  u  sA   ø‡ € ñGðP "×4Ñ4€Mòò=ò)ò(ò!ò
%÷.ð .r7   r
  Úlevyc                   óf   a € ] tR tRt o Rt]P                  tR tR t	R t
R tR tR tR	 tR
tV tR# )Ú
levy_l_geniÝ  aÓ  A left-skewed Levy continuous random variable.

%(before_notes)s

See Also
--------
levy, levy_stable

Notes
-----
The probability density function for `levy_l` is:

.. math::
    f(x) = \frac{1}{|x| \sqrt{2\pi |x|}} \exp{ \left(-\frac{1}{2|x|} \right)}

for :math:`x < 0`.

This is the same as the Levy-stable distribution with :math:`a=1/2` and
:math:`b=-1`.

%(after_notes)s

Examples
--------
>>> import numpy as np
>>> from scipy.stats import levy_l
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

>>> mean, var, skew, kurt = levy_l.stats(moments='mvsk')

Display the probability density function (``pdf``):

>>> # `levy_l` is very heavy-tailed.
>>> # To show a nice plot, let's cut off the lower 40 percent.
>>> a, b = levy_l.ppf(0.4), levy_l.ppf(1)
>>> x = np.linspace(a, b, 100)
>>> ax.plot(x, levy_l.pdf(x),
...        'r-', lw=5, alpha=0.6, label='levy_l pdf')

Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = levy_l()
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = levy_l.ppf([0.001, 0.5, 0.999])
>>> np.allclose([0.001, 0.5, 0.999], levy_l.cdf(vals))
True

Generate random numbers:

>>> r = levy_l.rvs(size=1000)

And compare the histogram:

>>> # manual binning to ignore the tail
>>> bins = np.concatenate(([np.min(r)], np.linspace(a, b, 20)))
>>> ax.hist(r, bins=bins, density=True, histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úlevy_l_gen._shape_info'  r¼   r7   c                óê   € \        V4      p^\        P                  ! ^\        P                  ,          V,          4      ,          V,          \        P                  ! R^V,          ,          4      ,          # rÓ  )r	  rQ   r'  r  rÓ   ©rD   rt   rº  s   && r5   ru   Úlevy_l_gen._pdf*  sF   € ä�‹VˆØ”—’˜œ2Ÿ5™5� �Ó$Õ$ RÕ'¬¯ª¨r°1°Rµ4­yÓ(9Õ9Ð9r7   c                ó€   € \        V4      p^\        ^\        P                  ! V4      ,          4      ,          ^,
          # rD  )r	  rÜ   rQ   r'  r1
  s   && r5   ry   Úlevy_l_gen._cdf/  s,   € Ü�‹VˆØ”9˜Q¤§¢¨£�_Ó-Õ-°Õ1Ð1r7   c                ór   € \        V4      p^\        ^\        P                  ! V4      ,          4      ,          # rD  )r	  ræ   rQ   r'  r1
  s   && r5   r~   Úlevy_l_gen._sf3  s'   € Ü�‹VˆØ”8˜A¤§¢¨£�OÓ,Õ,Ð,r7   c                óR   € \        VR ,           ^,          4      pRW",          ,          # rš  rë   r#
  s   && r5   r„   Úlevy_l_gen._ppf7  s!   € Ü˜˜S� A�Ó&ˆØ�s•yÕ!Ð!r7   c                óB   € R\        V^,          4      ^,          ,          # rÓ  r  r¢  s   &&r5   rˆ   Úlevy_l_gen._isf;  s   € Ø”)˜A˜a�C“. !Õ#Õ#Ð#r7   c                ó~   € \         P                  \         P                  \         P                  \         P                  3# rO   rE  rl   s   &r5   r   Úlevy_l_gen._stats>  r  r7   r‹   Nr*
  r“   s   @r5   r-
  r-
  Ý  sA   ø‡ € ñFðN "×4Ñ4€Mòò:ò
2ò-ò"ò$÷.ð .r7   r-
  Úlevy_lc                   ó¢   a a€ ] tR tRt oRtR tRR ltR tR tR t	R t
R	 tR
 tR tR tR tR t]]! ]4      V 3R l4       4       tRtVtV ;t# )Úlogistic_geniE  a¯  A logistic (or Sech-squared) continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `logistic` is:

.. math::

    f(x) = \frac{\exp(-x)}
                {(1+\exp(-x))^2}

`logistic` is a special case of `genlogistic` with ``c=1``.

Remark that the survival function (``logistic.sf``) is equal to the
Fermi-Dirac distribution describing fermionic statistics.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úlogistic_gen._shape_info]  r¼   r7   c                ó&   € VP                  VR 7      # rà  )Úlogisticró   s   &&&r5   rö   Úlogistic_gen._rvs`  s   € Ø×$Ñ$¨$Ð$Ó/Ð/r7   c                óL   € \         P                  ! V P                  V4      4      # rO   r.  r¿   s   &&r5   ru   Úlogistic_gen._pdfc  ry  r7   c                ó    € \         P                  ! V4      ) pVR \        P                  ! \         P                  ! V4      4      ,          ,
          # rr  )rQ   r	  r|   ré  rÓ   )rD   rt   rv  s   && r5   rý   Úlogistic_gen._logpdfg  s2   € Ü�VŠV�A‹YˆJˆØ�2œŸš¤§¢¨£Ó+Õ+Õ+Ð+r7   c                ó.   € \         P                  ! V4      # rO   rö  r¿   s   &&r5   ry   Úlogistic_gen._cdfk  ó   € Ü�xŠx˜‹{Ðr7   c                ó.   € \         P                  ! V4      # rO   ©r|   Ú	log_expitr¿   s   &&r5   r  Úlogistic_gen._logcdfn  s   € Ü�|Š|˜A‹Ðr7   c                ó.   € \         P                  ! V4      # rO   rû  rÉ   s   &&r5   r„   Úlogistic_gen._ppfq  rK
  r7   c                ó0   € \         P                  ! V) 4      # rO   rö  r¿   s   &&r5   r~   Úlogistic_gen._sft  s   € Ü�xŠx˜˜‹|Ðr7   c                ó0   € \         P                  ! V) 4      # rO   rM
  r¿   s   &&r5   r
  Úlogistic_gen._logsfw  s   € Ü�|Š|˜Q˜BÓÐr7   c                ó0   € \         P                  ! V4      ) # rO   rû  rÉ   s   &&r5   rˆ   Úlogistic_gen._isfz  s   € Ü—’˜“ˆ|Ðr7   c                ób   € ^ \         P                  \         P                  ,          R,          ^ R3# )r   r£  g333333ó?r`  rl   s   &r5   r   Úlogistic_gen._stats}  s!   € Ø”"—%‘%œŸ™•+˜c•/ 1 gÐ-Ð-r7   c                ó   € R # rr  r‹   rl   s   &r5   r  Úlogistic_gen._entropy€  s   € ár7   c                óÈ  <aa
aa€ VP                  R R4      '       d   \        SV `  ! S.VO5/ VB # \        V SW#4      w  orE\	        S4      oV P                  S4      w  rgVP                  RV4      VP                  RV4      rvV3VV3R llo
V3VV3R lloV
V3R lpVe3   Vf/   \        P                  ! S
V34      p	V	P                  ^ ,          pTpM\Ve3   Vf/   \        P                  ! SV34      p	V	P                  ^ ,          pTpM&\        P                  ! W†V34      p	V	P                  w  rg\        V4      pV	P                  '       d   Wg3# \        SV `  ! S.VO5/ VB # )rE  Fr-   r.   c                 ó”   <€ SV ,
          V,          p\         P                  ! \        P                  ! V4      4      S^,          ,
          # rD  )rQ   rè  r|   r÷  )r-   r.   r\  rE   rc   s   && €€r5   Údl_dlocÚ!logistic_gen.fit.<locals>.dl_dloc˜  s1   ø€ Ø˜•˜uÕ$ˆAÜ—6’6œ"Ÿ(š( 1›+Ó&¨¨1­Õ,Ð,r7   c                 ó¢   <€ SV,
          V ,          p\         P                  ! V\         P                  ! V^,          4      ,          4      S,
          # rD  )rQ   rè  rï  )r.   r-   r\  rE   rc   s   && €€r5   Ú	dl_dscaleÚ#logistic_gen.fit.<locals>.dl_dscaleœ  s5   ø€ Ø˜•˜uÕ$ˆAÜ—6’6˜!œBŸGšG A a¥C›L�.Ó)¨AÕ-Ð-r7   c                 ó,   <€ V w  rS! W4      S! W!4      3# rO   r‹   )Úparamsr-   r.   r^
  ra
  s   &  €€r5   r˜  Úlogistic_gen.fit.<locals>.func   s   ø€ Ø‰JˆCÙ˜3Ó&©	°%Ó(=Ð=Ð=r7   )r2   r@   rB   rR  rç  r×  r<   r   rS  rt   r	  Úsuccess)rD   rE   rF   r4   r  r  r-   r.   r˜  r›  r^
  ra
  rc   rØ  s   &f*,      @@@€r5   rB   Úlogistic_gen.fit„  sT  ü€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä8¸¸tØ9=óEÑˆˆdä�‹Iˆð —^‘^ DÓ)‰
ˆà—X‘X˜e SÓ)¨4¯8©8°G¸UÓ+CˆUð  &÷ 	-ð 	-ð "&÷ 	.ð 	.ö	>ð Ò $¢,Ü—-’- ¨#¨Ó0ˆCØ—%‘%˜•(ˆCØ‰EØÒ &¢.Ü—-’- 	¨E¨8Ó4ˆCØ—E‘E˜!•HˆEØ‰Cä—-’- ¨E lÓ3ˆCØŸ™‰JˆCô �E“
ˆØ #§§ ��ð 	7Ü‘W’[ Ð5¨Ò5°Ñ5ð	7r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r  r„   r~   r
  rˆ   r   r  rK   r   r   rB   r‘   r’   r  r   s   @@r5   r?
  r?
  E  sl   ù‡ € ñò.ô0ò'ò,òòòòò òò.òð Ù˜MÓ*ô07ó +ó ÷07ð 07r7   r?
  rC
  c                   ód   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tRtV tR# )Úloggamma_geni¼  a‰  A log gamma continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `loggamma` is:

.. math::

    f(x, c) = \frac{\exp(c x - \exp(x))}
                   {\Gamma(c)}

for all :math:`x, c > 0`. Here, :math:`\Gamma` is the
gamma function (`scipy.special.gamma`).

`loggamma` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úloggamma_gen._shape_infoÕ  r6  r7   Nc                óÂ   € \         P                  ! VP                  V^,           VR7      4      \         P                  ! VP                  VR7      4      V,          ,           # )rM   r³  )rQ   r  r(  r´  rÖ  s   &&&&r5   rö   Úloggamma_gen._rvsØ  sM   € ô —’�|×)Ñ)¨!¨a­%°dÐ)Ó;Ó<Ü—&’&˜×-Ñ-°4Ð-Ó8Ó9¸!Õ;õ<ð 	=r7   c                ó¦   € \         P                  ! W!,          \         P                  ! V4      ,
          \        P                  ! V4      ,
          4      # rO   ©rQ   rÓ   r|   r  r`  s   &&&r5   ru   Úloggamma_gen._pdfæ  s,   € ä�vŠv�a•cœ"Ÿ&š& ›)•m¤B§J¢J¨q£MÕ1Ó2Ð2r7   c                ó~   € W!,          \         P                  ! V4      ,
          \        P                  ! V4      ,
          # rO   ro
  r`  s   &&&r5   rý   Úloggamma_gen._logpdfê  s#   € Ø�s”R—V’V˜A“Y�¤§¢¨A£Õ.Ð.r7   c                óH   € \         P                  ! V\        8  W3R  R 4      # )c                 ó~   € \         P                  ! W,          \        P                  ! V^,           4      ,
          4      # r_   ro
  rÔ  s   &&r5   r  Ú#loggamma_gen._cdf.<locals>.<lambda>þ  s    € œŸš ¥¤b§j¢j°°1µ£oÕ 5Ô6r7   c                 óX   € \         P                  ! V\        P                  ! V 4      4      # rO   )r|   rB  rQ   rÓ   rÔ  s   &&r5   r  ru
  ÿ  s   € œŸš Q¬¯ª¨q«	Ô2r7   ©r  r  r"   r`  s   &&&r5   ry   Úloggamma_gen._cdfí  s&   € ô �ŠØ”‰L˜1˜&Ù6Ù2ó4ð 	4r7   c                óv   € \         P                  ! W!4      p\        P                  ! V\        8  W1V3R  R 4      # )c                 ó€   € \         P                  ! V4      \        P                  ! V^,           4      ,           V,          # r_   r_  ©rI  rƒ   r\  s   &&&r5   r  Ú#loggamma_gen._ppf.<locals>.<lambda>  s"   € œRŸVšV A›Y¬¯ª°A°aµC«Õ8¸!Ö;r7   c                 ó.   € \         P                  ! V 4      # rO   rc  r{
  s   &&&r5   r  r|
    ó   € œBŸFšF 1œIr7   )r|   rK  r  r  r!   ©rD   rƒ   r\  rI  s   &&& r5   r„   Úloggamma_gen._ppf  s6   € ô �NŠN˜1Ó ˆÜ�ŠØ”‰I˜˜a�yÙ;Ù%ó'ð 	'r7   c                óH   € \         P                  ! V\        8  W3R  R 4      # )c                 ó€   € \         P                  ! W,          \        P                  ! V^,           4      ,
          4      ) # r_   )rQ   rf  r|   r  rÔ  s   &&r5   r  Ú"loggamma_gen._sf.<locals>.<lambda>  s#   € œ"Ÿ(š( 1¥3¬¯ª°A°aµC«Õ#8Ó9Ñ9r7   c                 óX   € \         P                  ! V\        P                  ! V 4      4      # rO   )r|   rF  rQ   rÓ   rÔ  s   &&r5   r  rƒ
    s   € œŸš a¬¯ª°«Ô3r7   rw
  r`  s   &&&r5   r~   Úloggamma_gen._sf
  s$   € ä�ŠØ”‰L˜1˜&Ù9Ù3ó5ð 	5r7   c                óv   € \         P                  ! W!4      p\        P                  ! V\        8  W1V3R  R 4      # )c                 ó‚   € \         P                  ! V) 4      \        P                  ! V^,           4      ,           V,          # r_   )rQ   ré  r|   r  r{
  s   &&&r5   r  Ú#loggamma_gen._isf.<locals>.<lambda>  s$   € œRŸXšX q b›\¬B¯JªJ°q¸µs«OÕ;¸QÖ>r7   c                 ó.   € \         P                  ! V 4      # rO   rc  r{
  s   &&&r5   r  rˆ
    r~
  r7   )r|   rP  r  r  r!   r
  s   &&& r5   rˆ   Úloggamma_gen._isf  s6   € ô �OŠO˜AÓ!ˆÜ�ŠØ”‰I˜˜a�yÙ>Ù%ó'ð 	'r7   c                ó  € \         P                  ! V4      p\         P                  ! ^V4      p\         P                  ! ^V4      \        P                  ! VR4      ,          p\         P                  ! ^V4      W3,          ,          pW#WE3# rG  )r|   rZ  Ú	polygammarQ   rU  )rD   r\  r&  rê  rB	  Úexcess_kurtosiss   &&    r5   r   Úloggamma_gen._stats  sc   € ô �zŠz˜!‹}ˆÜ�lŠl˜1˜aÓ ˆÜ—<’<  1Ó%¬¯ª°°cÓ(:Õ:ˆÜŸ,š, q¨!Ó,°µÕ8ˆØ˜(Ð3Ð3r7   c                óD   € R  pR p\         P                  ! V^-8¬  WV4      # )c                 ó„   € \         P                  ! V 4      V \         P                  ! V 4      ,          ,
          V ,           pV# rO   )r|   r  rZ  )r\  r‰  s   & r5   ró  Ú&loggamma_gen._entropy.<locals>.regular$  s+   € Ü—
’
˜1“ ¤B§J¢J¨q£MÕ 1Õ1°AÕ5ˆAØˆHr7   c                 óô   € R\         P                  ! V 4      ,          V R,          ^,          ,           V R,          ^Z,          ,
          V R,          ^Ò,          ,           p\        P                  4       V,           pV# )r£   r#  r›  r÷  r  )rQ   r  r/  r  )r\  Útermr‰  s   &  r5   rì  Ú)loggamma_gen._entropy.<locals>.asymptotic(  sO   € àœŸš˜q›	•> A s¥F¨1¥HÕ,¨q°#­v°b­yÕ8¸1¸c½6À#½:ÕEˆDÜ—‘“ $Õ&ˆAØˆHr7   r=  )rD   r\  ró  rì  s   &&  r5   r  Úloggamma_gen._entropy#  s%   € ò	ò	ô �Š˜q B™w¨°wÓ?Ð?r7   r‹   r.  ©rŒ   r�   rŽ   r�   r�   rm   rö   ru   rý   ry   r„   r~   rˆ   r   r  r‘   r’   r“   s   @r5   ri
  ri
  ¼  sD   ø‡ € ñò0Eô=ò3ò/ò4ò('ò5ò'ò4÷@ð @r7   ri
  Úloggammac                   ó†   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 t]]! ]4      V 3R l4       4       tRtVtV ;t# )Úloglaplace_geni4  a  A log-Laplace continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `loglaplace` is:

.. math::

    f(x, c) = \begin{cases}\frac{c}{2} x^{ c-1}  &\text{for } 0 < x < 1\\
                           \frac{c}{2} x^{-c-1}  &\text{for } x \ge 1
              \end{cases}

for :math:`c > 0`.

`loglaplace` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

Suppose a random variable ``X`` follows the Laplace distribution with
location ``a`` and scale ``b``.  Then ``Y = exp(X)`` follows the
log-Laplace distribution with ``c = 1 / b`` and ``scale = exp(a)``.

References
----------
T.J. Kozubowski and K. Podgorski, "A log-Laplace growth rate model",
The Mathematical Scientist, vol. 28, pp. 49-60, 2003.

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úloglaplace_gen._shape_infoU  r6  r7   c                óv   € VR ,          p\         P                  ! V^8  W") 4      pW1V^,
          ,          ,          # rr  ©rQ   r±  )rD   rt   r\  Úcd2s   &&& r5   ru   Úloglaplace_gen._pdfX  s3   € ð ��eˆÜ�HŠH�Q˜‘U˜A˜rÓ"ˆØ�q˜•s•8�|Ðr7   c                ó|   € \         P                  ! V^8  RW,          ,          ^RW) ,          ,          ,
          4      # r 	  r�
  r`  s   &&&r5   ry   Úloglaplace_gen._cdf_  s+   € Ü�xŠx˜˜A™˜s 1¥4�x¨¨3¨q°2­w­;­Ó7Ð7r7   c                ó|   € \         P                  ! V^8  ^RW,          ,          ,
          RW) ,          ,          4      # r 	  r�
  r`  s   &&&r5   r~   Úloglaplace_gen._sfb  s+   € Ü�xŠx˜˜A™˜q 3 q¥t¥8�|¨S°°Rµ­[Ó9Ð9r7   c                óš   € \         P                  ! VR 8  RV,          RV,          ,          ^RV,
          ,          RV,          ,          4      # ©r£   rÒ   r–   r›  r�
  rg  s   &&&r5   r„   Úloglaplace_gen._ppfe  s7   € Ü�xŠx˜˜C™ # a¥%¨3¨q­5Õ!1°A°s¸1µuµIÀÀaÅÕ3HÓIÐIr7   c                óš   € \         P                  ! VR 8„  RRV,
          ,          RV,          ,          ^V,          RV,          ,          4      # r¥
  r�
  rg  s   &&&r5   rˆ   Úloglaplace_gen._isfh  s6   € Ü�xŠx˜˜C™ # s¨Q¥w¥-°3°qµ5Õ!9¸A¸a½CÀ4ÈÅ6½?ÓKÐKr7   c                ó
  € \         P                  ! R R7      ;_uu_ 4        V^,          V^,          rC\         P                  ! WC8  W3V,
          ,          \         P                  4      uuRRR4       #   + '       g   i     R# ; i©rl  rm  N)rQ   ro  r±  rk   )rD   rc   r\  rÇ  Ún2s   &&&  r5   r,  Úloglaplace_gen._munpk  sK   € Ü�[Š[ ×)Ö)Ø˜•T˜1˜a�4�Ü—8’8˜B™G R°­7¥^´R·V±VÓ<÷ *×)×)Ó)ús    AA1Á1B	c                óJ   € \         P                  ! R V,          4      R,           # r  rc  r÷  s   &&r5   r  Úloglaplace_gen._entropyp  s   € Ü�vŠv�c˜!•e‹}˜sÕ"Ð"r7   c                ó  <€ \        WW#4      w  rrVVf   \        \        V 4      V `  ! V.VO5/ VB # \        P
                  ! W8*  4      '       d   \        RV\        P                  R7      hV^ 8w  d	   W,
          p\        P                  \        P                  ! V4      Ve   \        P                  ! V4      MR Ve
   ^V,          MR RR7      w  rxTp	Vf   \        P                  ! V4      MTp
Vf
   ^V,          MTpW¹V
3# )NÚ
loglaplacerÛ  r:   )r  r  r0   )rR  r@   rA   rB   rQ   ræ  rƒ  rk   rÐ	  r  rÓ   )rD   rE   rF   r4   rT  r  r  r˜   r™   r-   r.   r\  rØ  s   &&*,        €r5   rB   Úloglaplace_gen.fits  sí   ø€ ô "=¸TØ=Aó"IÑˆ�$ð Š<Üœ˜d› TÒ.¨tÐC°dÒC¸dÑCÐCô �6Š6�$‘,×ÒÜ˜|°4¼r¿v¹vÔFÐFð �1Œ9Ø•;ˆDô �{‰{œ2Ÿ6š6 $›<Ø28Ò2D¤§¢ v¤È$Ø*,ª. ! B¦$¸dØ"'ð ó )‰ˆð ˆØ#š^”—’�q”	°ˆØ’ZˆA�ŽE RˆØ�uˆ}Ðr7   r‹   )rŒ   r�   rŽ   r�   r�   rm   ru   ry   r~   r„   rˆ   r,  r  rK   r   r   rB   r‘   r’   r  r   s   @@r5   r™
  r™
  4  s\   ù‡ € ñò@Eòò8ò:òJòLò=ò
#ð Ù˜MÓ*ôó +ó ÷ð r7   r™
  r°
  c                 ó^   € \         P                  ! V ^ 8g  W3R \        P                  ) R7      # )r   c                 ó
  € \         P                  ! V 4      ^,          ) ^V^,          ,          ,          \         P                  ! W,          \         P                  ! ^\         P                  ,          4      ,          4      ,
          # rD  )rQ   r  r'  r  ©rt   rj  s   &&r5   r  Ú!_lognorm_logpdf.<locals>.<lambda>š  sH   € ”r—v’v˜a“y !•|�m q¨1¨a­4¥xÕ0ÜŸš˜q�u¤r§w¢w¨q´2·5±5­yÓ'9Õ9Ó:ö;r7   r  rU  r´
  s   &&r5   Ú_lognorm_logpdfr¶
  —  s,   € Ü�?Š?Ø	ˆQ‰��ñ	<ä—F‘F�7ô	ð r7   c                   ó¾   a a€ ] tR tRt oRt]P                  tR tRR lt	R t
R tR tR tR	 tR
 tR tR tR tR t]]! ]RR7      V 3R l4       4       tRtVtV ;t# )Úlognorm_geniŸ  a9  A lognormal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `lognorm` is:

.. math::

    f(x, s) = \frac{1}{s x \sqrt{2\pi}}
              \exp\left(-\frac{\log^2(x)}{2s^2}\right)

for :math:`x > 0`, :math:`s > 0`.

`lognorm` takes ``s`` as a shape parameter for :math:`s`.

%(after_notes)s

Suppose a normally distributed random variable ``X`` has  mean ``mu`` and
standard deviation ``sigma``. Then ``Y = exp(X)`` is lognormally
distributed with ``s = sigma`` and ``scale = exp(mu)``.

%(example)s

The logarithm of a log-normally distributed random variable is
normally distributed:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy import stats
>>> fig, ax = plt.subplots(1, 1)
>>> mu, sigma = 2, 0.5
>>> X = stats.norm(loc=mu, scale=sigma)
>>> Y = stats.lognorm(s=sigma, scale=np.exp(mu))
>>> x = np.linspace(*X.interval(0.999))
>>> y = Y.rvs(size=10000)
>>> ax.plot(x, X.pdf(x), label='X (pdf)')
>>> ax.hist(np.log(y), density=True, bins=x, label='log(Y) (histogram)')
>>> ax.legend()
>>> plt.show()

c                ó@   € \        R R^ \        P                  3R4      .# )rj  Fr4  rj   rl   s   &r5   rm   Úlognorm_gen._shape_infoÍ  r6  r7   c                óX   € \         P                  ! WP                  V4      ,          4      # rO   ©rQ   rÓ   rò   )rD   rj  rô   rõ   s   &&&&r5   rö   Úlognorm_gen._rvsÐ  s   € Ü�vŠv�a×6Ñ6°tÓ<Õ<Ó=Ð=r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  ©rD   rt   rj  s   &&&r5   ru   Úlognorm_gen._pdfÓ  r™  r7   c                ó   € \        W4      # rO   ©r¶
  r¿
  s   &&&r5   rý   Úlognorm_gen._logpdf×  s   € Ü˜qÓ$Ð$r7   c                óN   € \        \        P                  ! V4      V,          4      # rO   ©rÜ   rQ   r  r¿
  s   &&&r5   ry   Úlognorm_gen._cdfÚ  s   € ÜœŸš › Q�Ó'Ð'r7   c                óN   € \        \        P                  ! V4      V,          4      # rO   rb  r¿
  s   &&&r5   r  Úlognorm_gen._logcdfÝ  s   € ÜœBŸFšF 1›I¨�MÓ*Ð*r7   c                óN   € \         P                  ! V\        V4      ,          4      # rO   ©rQ   rÓ   rã   ©rD   rƒ   rj  s   &&&r5   r„   Úlognorm_gen._ppfà  ó   € Ü�vŠv�aœ) A›,Õ&Ó'Ð'r7   c                óN   € \        \        P                  ! V4      V,          4      # rO   ©ræ   rQ   r  r¿
  s   &&&r5   r~   Úlognorm_gen._sfã  s   € ÜœŸš˜q›	 A�Ó&Ð&r7   c                óN   € \        \        P                  ! V4      V,          4      # rO   )ré   rQ   r  r¿
  s   &&&r5   r
  Úlognorm_gen._logsfæ  s   € Üœ2Ÿ6š6 !›9 q�=Ó)Ð)r7   c                óN   € \         P                  ! V\        V4      ,          4      # rO   ©rQ   rÓ   rì   rË
  s   &&&r5   rˆ   Úlognorm_gen._isfé  rÍ
  r7   c                ó  € \         P                  ! W,          4      p\         P                  ! V4      pW"^,
          ,          p\         P                  ! V^,
          4      ^V,           ,          p\         P                  ! . ROV4      pW4WV3# ©rM   )rM   rÑ   r¦  r   r  )rQ   rÓ   r'  Úpolyval)rD   rj  rH  ry  rz  r{  r|  s   &&     r5   r   Úlognorm_gen._statsì  s^   € Ü�FŠF�1•3‹KˆÜ�WŠW�Q‹ZˆØ�1•�gˆÜ�WŠW�Q�q•S‹\˜1˜Q�3ÕˆÜ�ZŠZÒ*¨AÓ.ˆØ˜ˆÐr7   c                ó¸   € R ^\         P                  ! ^\         P                  ,          4      ,           ^\         P                  ! V4      ,          ,           ,          # r  r  )rD   rj  s   &&r5   r  Úlognorm_gen._entropyô  s3   € Ø�aœ"Ÿ&š& ¤2§5¡5¥›/Õ)¨A´·²°q³	­MÕ9Õ:Ð:r7   aF          When `method='MLE'` and
        the location parameter is fixed by using the `floc` argument,
        this function uses explicit formulas for the maximum likelihood
        estimation of the log-normal shape and scale parameters, so the
        `optimizer`, `loc` and `scale` keyword arguments are ignored.
        If the location is free, a likelihood maximum is found by
        setting its partial derivative wrt to location to 0, and
        solving by substituting the analytical expressions of shape
        and scale (or provided parameters).
        See, e.g., equation 3.1 in
        A. Clifford Cohen & Betty Jones Whitten (1980)
        Estimation in the Three-Parameter Lognormal Distribution,
        Journal of the American Statistical Association, 75:370, 399-404
        https://doi.org/10.2307/2287466
        

r  c                ó  <a aaaa€ VP                  R R4      '       d   \        SS `  ! S.VO5/ VB # \        S SW#4      pVw  oopo\        P
                  ! S4      pVVV3R loVV3R lpVVV 3R lpVEf/   \        P                  ! V4      p	Wi,
          p
V! V
4      pV! V
4      p^V	,          pVR	8¼  d   Wm,
          p
V! V
4      pV^,          pK"  \        P                  ! V
4      '       d   \        P                  ! V4      '       g   \        SS `  ! S.VO5/ VB # \        P                  ! \        P                  ! V
\        P                  ) 4      V
^,
          4      pV! V4      p^W®,
          ,          p\        P                  ! V4      '       dg   \        P                  ! V4      '       dK   \        P                  ! V4      \        P                  ! V4      8X  d   W­,
          pV! V4      pV^,          pK‚  \        P                  ! V4      '       d   \        P                  ! V4      '       g   \        SS `  ! S.VO5/ VB # \        W~V
3R7      pVP                  '       g   \        SS `  ! S.VO5/ VB # V! VP                  4      pVV8”  d   VP                  MWi,
          pM$WV8¼  d   \        RR\        P                  R7      hTpS! V4      w  ppS P!                  V4      '       d   V^ 8”  g   \        SS `  ! S.VO5/ VB # VVV3# )
rE  Fc                 ó\  <€ Se   Sf   \         P                  ! SV ,
          4      pS;'       g%    \         P                  ! XP                  4       4      pS;'       gM    \         P                  ! \         P                  ! X\         P                  ! V4      ,
          ^,          4      4      pW23# rO   )rQ   r  rÓ   r&  r'  )r-   Úlndatar.   rG  rE   r  Úfshapes   &   €€€r5   Úget_shape_scaleÚ(lognorm_gen.fit.<locals>.get_shape_scale  su   ø€ ð Š~ ¢ÜŸš  s¥
Ó+�Ø×3Ð3œbŸfšf V§[¡[£]Ó3ˆEØ×KÐKœbŸgšg¤b§g¢g¨v¼¿º¸u»Õ/EÈÕ.IÓ&JÓKˆEØ�<Ðr7   c                 óÂ   <€ S! V 4      w  rSV ,
          p\         P                  ! ^\         P                  ! W2,          4      V^,          ,          ,           V,          4      # r_   ©rQ   rè  r  )r-   rG  r.   ÚshiftedrE   rà
  s   &   €€r5   ÚdL_dLocÚ lognorm_gen.fit.<locals>.dL_dLoc  sE   ø€ á*¨3Ó/‰LˆEØ˜S•jˆGÜ—6’6˜1œrŸvšv g¥mÓ4°U¸AµXÕ=Õ=¸wÕFÓGÐGr7   c                 óB   <€ S! V 4      w  rSP                  WV3S4      ) # rO   )Únnlf)r-   rG  r.   rE   rà
  rD   s   &  €€€r5   ÚllÚlognorm_gen.fit.<locals>.ll  s(   ø€ á*¨3Ó/‰LˆEØ—I‘I˜u¨5Ð1°4Ó8Ð8Ð8r7   rÜ  Úlognormr•   rÛ  g�íµ ÷Æ°¾)r2   r@   rB   rR  rQ   rR  Úspacingr$  r  Ú	nextafterrk   rR   r*   Ú	convergedrS  rƒ  rd   )rD   rE   rF   r4   Ú
parametersr  rS  rå
  ré
  rì
  rT   ÚdL_dLoc_rbrackÚ	ll_rbrackr6	  rS   ÚdL_dLoc_lbrackr›  Úll_rootr-   rG  r.   r  rß
  rà
  rØ  s   ff*,                 @@@€r5   rB   Úlognorm_gen.fit÷  s‚  ý€ ð$ �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä0°°t¸TÓHˆ
Ø%/Ñ"ˆˆf�d˜FÜ—6’6˜$“<ˆ÷	 ö	H÷	9ð
 ‹<ô —j’j Ó*ˆGØÕ'ˆFñ % V›_ˆNÙ˜6›
ˆIØ˜•KˆEØ  EÔ)Ø!Õ)�Ù!(¨£�Ø˜•
’ä—;’;˜v×&Ò&¬b¯kªk¸.×.IÒ.Iô ‘w’{ 4Ð7¨$Ò7°$Ñ7Ð7ô
 —Z’Z¤§¢¨V´b·f±f°WÓ =¸vÀa½xÓHˆFÙ$ V›_ˆNØ˜�Õ)ˆEÜ—;’;˜v×&Ò&¬2¯;ª;°~×+FÒ+FÜ—w’w˜~Ó.´"·'²'¸.Ó2IÔIØ��Ù!(¨£�Ø˜•
’ô —;’;˜v×&Ò&¬b¯kªk¸.×.IÒ.IÜ‘w’{ 4Ð7¨$Ò7°$Ñ7Ð7ô ˜g¸Ð/?Ô@ˆCØ—=—=�=Ü‘w’{ 4Ð7¨$Ò7°$Ñ7Ð7ñ
 ˜Ÿ™“lˆGØ%¨	Ô1�#—(’(°xÕ7G‰Cð ÔÜ" 9°B¼b¿f¹fÔEÐEØˆCá& sÓ+‰ˆˆuØ—‘˜u×%Ò%¨%°!¬)Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3Ø�c˜5Ð Ð r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   rö   ru   rý   ry   r  r„   r~   r
  rˆ   r   r  rK   r	   rB   r‘   r’   r  r   s   @@r5   r¸
  r¸
  Ÿ  s…   ù‡ € ñ*ðV "×4Ñ4€MòEô>ò*ò%ò(ò+ò(ò'ò*ò(òò;ð Ù˜}ð 5ô ô Z!ó!ó ÷"Z!ð Z!r7   r¸
  rë
  c                   ó|   a € ] tR tRt o Rt]P                  tR tRR lt	R t
R tR tR	 tR
 tR tR tR tRtV tR# )Ú
gibrat_genih  a/  A Gibrat continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `gibrat` is:

.. math::

    f(x) = \frac{1}{x \sqrt{2\pi}} \exp(-\frac{1}{2} (\log(x))^2)

for :math:`x >= 0`.

`gibrat` is a special case of `lognorm` with ``s=1``.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úgibrat_gen._shape_info€  r¼   r7   Nc                óL   € \         P                  ! VP                  V4      4      # rO   r¼
  ró   s   &&&r5   rö   Úgibrat_gen._rvsƒ  s   € Ü�vŠv�l×2Ñ2°4Ó8Ó9Ð9r7   c                óL   € \         P                  ! V P                  V4      4      # rO   r.  r¿   s   &&r5   ru   Úgibrat_gen._pdf†  ry  r7   c                ó   € \        VR 4      # r8  rÂ
  r¿   s   &&r5   rý   Úgibrat_gen._logpdfŠ  s   € Ü˜q #Ó&Ð&r7   c                ó@   € \        \        P                  ! V4      4      # rO   rÅ
  r¿   s   &&r5   ry   Úgibrat_gen._cdf�  s   € ÜœŸš ›Ó#Ð#r7   c                ó@   € \         P                  ! \        V4      4      # rO   rÊ
  rÉ   s   &&r5   r„   Úgibrat_gen._ppf�  ó   € Ü�vŠv”i “lÓ#Ð#r7   c                ó@   € \        \        P                  ! V4      4      # rO   rÏ
  r¿   s   &&r5   r~   Úgibrat_gen._sf“  s   € ÜœŸš˜q›	Ó"Ð"r7   c                ó@   € \         P                  ! \        V4      4      # rO   rÔ
  r¢  s   &&r5   rˆ   Úgibrat_gen._isf–  r  r7   c                óü   € \         P                  p\         P                  ! V4      pW^,
          ,          p\         P                  ! V^,
          4      ^V,           ,          p\         P                  ! . ROV4      pW#WE3# r×
  )rQ   Úer'  rØ
  )rD   rH  ry  rz  r{  r|  s   &     r5   r   Úgibrat_gen._stats™  sX   € Ü�D‰DˆÜ�WŠW�Q‹ZˆØ�q•5�kˆÜ�WŠW�Q˜•U‹^˜q 1�uÕ%ˆÜ�ZŠZÒ*¨AÓ.ˆØ˜ˆÐr7   c                ót   € R \         P                  ! ^\         P                  ,          4      ,          R ,           # r  r  rl   s   &r5   r  Úgibrat_gen._entropy¡  s#   € Ø”R—V’V˜A¤§¡�IÓ&Õ&¨Õ,Ð,r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   rö   ru   rý   ry   r„   r~   rˆ   r   r  r‘   r’   r“   s   @r5   rö
  rö
  h  sN   ø‡ € ñð* "×4Ñ4€Mòô:ò'ò'ò$ò$ò#ò$ò÷-ð -r7   rö
  Úgibratc                   ód   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tRtV tR# )Úmaxwell_geni¨  a×  A Maxwell continuous random variable.

%(before_notes)s

Notes
-----
A special case of a `chi` distribution,  with ``df=3``, ``loc=0.0``,
and given ``scale = a``, where ``a`` is the parameter used in the
Mathworld description [1]_.

The probability density function for `maxwell` is:

.. math::

    f(x) = \sqrt{2/\pi}x^2 \exp(-x^2/2)

for :math:`x >= 0`.

%(after_notes)s

References
----------
.. [1] http://mathworld.wolfram.com/MaxwellDistribution.html

%(example)s
c                ó   € . # rO   r‹   rl   s   &r5   rm   Úmaxwell_gen._shape_infoÃ  r¼   r7   Nc                ó0   € \         P                  R WR7      # )r£  r'  ©re  r)  ró   s   &&&r5   rö   Úmaxwell_gen._rvsÆ  s   € Ü�w‰w�s ˆwÓAÐAr7   c                ó~   € \         V,          V,          \        P                  ! V) V,          R ,          4      ,          # rr  )r&   rQ   rÓ   r¿   s   &&r5   ru   Úmaxwell_gen._pdfÉ  s*   € ä˜qÕ  Õ"¤2§6¢6¨1¨"¨Q­$¨s­(Ó#3Õ3Ð3r7   c                óø   € \         P                  ! R R7      ;_uu_ 4        \        ^\         P                  ! V4      ,          ,           RV,          V,          ,
          uuRRR4       #   + '       g   i     R# ; i)rl  rm  r£   N)rQ   ro  r(   r  r¿   s   &&r5   rý   Úmaxwell_gen._logpdfÍ  sA   € ä�[Š[ ×)Ö)Ü&¨¬2¯6ª6°!«9­Õ4°s¸1µu¸QµwÕ>÷ *×)×)Ó)ús    =A(Á(A9	c                óJ   € \         P                  ! R W,          R,          4      # ©rS  rÒ   rA  r¿   s   &&r5   ry   Úmaxwell_gen._cdfÒ  s   € Ü�{Š{˜3 ¥ C¥Ó(Ð(r7   c                óf   € \         P                  ! ^\        P                  ! RV4      ,          4      # rU  rJ  rÉ   s   &&r5   r„   Úmaxwell_gen._ppfÕ  s!   € Ü�wŠw�qœŸš¨¨QÓ/Õ/Ó0Ð0r7   c                óJ   € \         P                  ! R W,          R,          4      # r  rE  r¿   s   &&r5   r~   Úmaxwell_gen._sfØ  s   € Ü�|Š|˜C ¥ S¥Ó)Ð)r7   c                óf   € \         P                  ! ^\        P                  ! RV4      ,          4      # rU  rO  rÉ   s   &&r5   rˆ   Úmaxwell_gen._isfÛ  s!   € Ü�wŠw�qœŸš¨¨aÓ0Õ0Ó1Ð1r7   c                ó"  € ^\         P                  ,          ^,
          p^\         P                  ! R\         P                  ,          4      ,          ^^\         P                  ,          ,
          \         P                  ! ^4      ^ ^
\         P                  ,          ,
          ,          VR,          ,          R\         P                  ,          \         P                  ,          ^ \         P                  ,          ,           R,
          VR,          ,          3# )r¦  rÒ   rS  i€  r³  ©rQ   r  r'  ©rD   r˜  s   & r5   r   Úmaxwell_gen._statsÞ  sš   € Ø”—‘�g�a�iˆØ”"—'’'˜#œbŸe™e�)Ó$Õ$Ø�!”B—E‘E•'•	Ü—’˜“
˜B˜r¤"§%¡%�x�KÕ(¨¨c­Õ1Ø”R—U‘U•œ2Ÿ5™5• 3¤r§u¡u¥9Õ,¨sÕ2°c¸3µhÕ>ð@ð 	@r7   c                óŠ   € \         R \        P                  ! ^\        P                  ,          4      ,          ,           R ,
          # r  )r#   rQ   r  r  rl   s   &r5   r  Úmaxwell_gen._entropyå  s'   € Ü˜œBŸFšF 1¤R§U¡U¥7›OÕ+Õ+¨CÕ/Ð/r7   r‹   r.  r–
  r“   s   @r5   r  r  ¨  sC   ø‡ € ñò4ôBò4ò?ò
)ò1ò*ò2ò@÷0ð 0r7   r  Úmaxwellc                   óH   a € ] tR tRt o RtR tR tR tR tR t	R t
R	tV tR
# )Ú
mielke_geniì  aŠ  A Mielke Beta-Kappa / Dagum continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `mielke` is:

.. math::

    f(x, k, s) = \frac{k x^{k-1}}{(1+x^s)^{1+k/s}}

for :math:`x > 0` and :math:`k, s > 0`. The distribution is sometimes
called Dagum distribution ([2]_). It was already defined in [3]_, called
a Burr Type III distribution (`burr` with parameters ``c=s`` and
``d=k/s``).

`mielke` takes ``k`` and ``s`` as shape parameters.

%(after_notes)s

References
----------
.. [1] Mielke, P.W., 1973 "Another Family of Distributions for Describing
       and Analyzing Precipitation Data." J. Appl. Meteor., 12, 275-280
.. [2] Dagum, C., 1977 "A new model for personal income distribution."
       Economie Appliquee, 33, 327-367.
.. [3] Burr, I. W. "Cumulative frequency functions", Annals of
       Mathematical Statistics, 13(2), pp 215-232 (1942).

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# )rk  Frj  r4  rj   )rD   ÚikÚi_ss   &  r5   rm   Úmielke_gen._shape_info  ó:   € Ü˜˜U Q¬¯© K°Ó@ˆÜ˜˜e a¬¯© [°.ÓAˆØˆyÐr7   c                óŽ   € W!VR ,
          ,          ,          R W,          ,           R VR ,          V,          ,           ,          ,          # r8  r‹   ©rD   rt   rk  rj  s   &&&&r5   ru   Úmielke_gen._pdf  s.   € Ø�Q�s•U•�|˜s 1¥4�x¨3¨q°­u°Q­w­;Õ7Õ7Ð7r7   c                óf  € \         P                  ! R R7      ;_uu_ 4        \         P                  ! V4      \         P                  ! V4      V^,
          ,          ,           \         P                  ! W,          4      ^W#,          ,           ,          ,
          uuRRR4       #   + '       g   i     R# ; irª
  )rQ   ro  r  ré  r1  s   &&&&r5   rý   Úmielke_gen._logpdf  s[   € ä�[Š[ ×)Ö)Ü—6’6˜!“9œrŸvšv a›y¨!¨a­%Õ0Õ0´2·8²8¸A½D³>À1ÀqÅsÅ7Õ3KÕK÷ *×)×)Ó)ús    A4BÂB0	c                ód   € W,          R W,          ,           VR ,          V,          ,          ,          # r8  r‹   r1  s   &&&&r5   ry   Úmielke_gen._cdf  s"   € Ø�t�s˜1�4•x 1 S¥5¨¥7Õ+Õ+Ð+r7   c                óv   € \        WR ,          V,          4      p\        VR V,
          ,          R V,          4      # r8  r:  )rD   rƒ   rk  rj  Úqsks   &&&& r5   r„   Úmielke_gen._ppf  s,   € Ü�!�s•U˜1•W‹oˆÜ�3˜˜C�•= # a¥%Ó(Ð(r7   c                ó`   € R  p\         P                  ! W8  WV3V\        P                  R7      # )c                 óÚ   € \         P                  ! W,           V,          4      \         P                  ! ^W,          ,
          4      ,          \         P                  ! W,          4      ,          # r_   r'  )rc   rk  rj  s   &&&r5   rv	  Ú$mielke_gen._munp.<locals>.nth_moment#  s9   € ä—8’8˜Q�S !�GÓ$¤R§X¢X¨a°µ­e£_Õ4´R·X²X¸a½c³]ÕBÐBr7   r  rU  )rD   rc   rk  rj  rv	  s   &&&& r5   r,  Úmielke_gen._munp"  s)   € ò	Cô �Š˜q™u q¨Q i°ÌÏÉÔOÐOr7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r,  r‘   r’   r“   s   @r5   r*  r*  ì  s1   ø‡ € ñ òBò
8òLò
,ò)÷Pð Pr7   r*  Úmielkec                   óf   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tR tRtV tR# )Ú
kappa4_geni-  a¤  Kappa 4 parameter distribution.

%(before_notes)s

Notes
-----
The probability density function for kappa4 is:

.. math::

    f(x, h, k) = (1 - k x)^{1/k - 1} (1 - h (1 - k x)^{1/k})^{1/h-1}

if :math:`h` and :math:`k` are not equal to 0.

If :math:`h` or :math:`k` are zero then the pdf can be simplified:

:math:`h = 0` and :math:`k \neq 0`::

    kappa4.pdf(x, h, k) = (1.0 - k*x)**(1.0/k - 1.0)*
                          exp(-(1.0 - k*x)**(1.0/k))

:math:`h \neq 0` and :math:`k = 0`::

    kappa4.pdf(x, h, k) = exp(-x)*(1.0 - h*exp(-x))**(1.0/h - 1.0)

:math:`h = 0` and :math:`k = 0`::

    kappa4.pdf(x, h, k) = exp(-x)*exp(-exp(-x))

kappa4 takes :math:`h` and :math:`k` as shape parameters.

The kappa4 distribution returns other distributions when certain
:math:`h` and :math:`k` values are used.

+------+-------------+----------------+------------------+
| h    | k=0.0       | k=1.0          | -inf<=k<=inf     |
+======+=============+================+==================+
| -1.0 | Logistic    |                | Generalized      |
|      |             |                | Logistic(1)      |
|      |             |                |                  |
|      | logistic(x) |                |                  |
+------+-------------+----------------+------------------+
|  0.0 | Gumbel      | Reverse        | Generalized      |
|      |             | Exponential(2) | Extreme Value    |
|      |             |                |                  |
|      | gumbel_r(x) |                | genextreme(x, k) |
+------+-------------+----------------+------------------+
|  1.0 | Exponential | Uniform        | Generalized      |
|      |             |                | Pareto           |
|      |             |                |                  |
|      | expon(x)    | uniform(x)     | genpareto(x, -k) |
+------+-------------+----------------+------------------+

(1) There are at least five generalized logistic distributions.
    Four are described here:
    https://en.wikipedia.org/wiki/Generalized_logistic_distribution
    The "fifth" one is the one kappa4 should match which currently
    isn't implemented in scipy:
    https://en.wikipedia.org/wiki/Talk:Generalized_logistic_distribution
    https://www.mathwave.com/help/easyfit/html/analyses/distributions/gen_logistic.html
(2) This distribution is currently not in scipy.

References
----------
J.C. Finney, "Optimization of a Skewed Logistic Distribution With Respect
to the Kolmogorov-Smirnov Test", A Dissertation Submitted to the Graduate
Faculty of the Louisiana State University and Agricultural and Mechanical
College, (August, 2004),
https://digitalcommons.lsu.edu/gradschool_dissertations/3672

J.R.M. Hosking, "The four-parameter kappa distribution". IBM J. Res.
Develop. 38 (3), 25 1-258 (1994).

B. Kumphon, A. Kaew-Man, P. Seenoi, "A Rainfall Distribution for the Lampao
Site in the Chi River Basin, Thailand", Journal of Water Resource and
Protection, vol. 4, 866-869, (2012).
:doi:`10.4236/jwarp.2012.410101`

C. Winchester, "On Estimation of the Four-Parameter Kappa Distribution", A
Thesis Submitted to Dalhousie University, Halifax, Nova Scotia, (March
2000).
http://www.nlc-bnc.ca/obj/s4/f2/dsk2/ftp01/MQ57336.pdf

%(after_notes)s

%(example)s

c                ó€   € \         P                  ! W4      ^ ,          P                  p\         P                  ! VRR7      # )r   Tr  )rQ   rE  rG  Úfull)rD   r‰  rk  rG  s   &&& r5   rd   Úkappa4_gen._argcheck†  s.   € Ü×#Ò# AÓ)¨!Õ,×2Ñ2ˆÜ�wŠw�u¨Ô.Ð.r7   c                ó¼   € \        R R\        P                  ) \        P                  3R4      p\        RR\        P                  ) \        P                  3R4      pW.# )r‰  Frk  r4  rj   )rD   Úihr,  s   &  r5   rm   Úkappa4_gen._shape_infoŠ  sG   € Ü˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆÜ˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆØˆxˆr7   c           
     ó  € \         P                  ! V^ 8„  V^ 8„  4      \         P                  ! V^ 8„  V^ 8H  4      \         P                  ! V^ 8„  V^ 8  4      \         P                  ! V^ 8*  V^ 8„  4      \         P                  ! V^ 8*  V^ 8H  4      \         P                  ! V^ 8*  V^ 8  4      .pR pR pR pR p\        VWEWFWg.W.\         P                  R7      pR pR p\        VWEWTWU.W.\         P                  R7      p	W‰3# )r   c                 óL   € R \         P                  ! W) 4      ,
          V,          # r8  )rQ   r;  ©r‰  rk  s   &&r5   rß  Ú#kappa4_gen._get_support.<locals>.f0—  s   € Øœ"Ÿ.š.¨¨BÓ/Õ/°Õ2Ð2r7   c                 ó.   € \         P                  ! V 4      # rO   rc  rI  s   &&r5   râ  Ú#kappa4_gen._get_support.<locals>.f1š  s   € Ü—6’6˜!“9Ðr7   c                 ó‚   € \         P                  ! \         P                  ! V 4      4      p\         P                  ) VR &   V# ©ºNNN©rQ   rØ  rG  rk   ©r‰  rk  r˜   s   && r5   Úf3Ú#kappa4_gen._get_support.<locals>.f3�  s,   € Ü—’œŸš !›Ó%ˆAÜ—F‘F�7ˆAˆa‰DØˆHr7   c                 ó   € R V,          # r8  r‹   rI  s   &&r5   Úf5Ú#kappa4_gen._get_support.<locals>.f5¢  ó   € Ø�q•5ˆLr7   ©Údefaultc                 ó   € R V,          # r8  r‹   rI  s   &&r5   rß  rJ  ª  rW  r7   c                 ó€   € \         P                  ! \         P                  ! V 4      4      p\         P                  VR &   V# rN  rP  rQ  s   && r5   râ  rL  ­  s*   € Ü—’œŸš !›Ó%ˆAÜ—6‘6ˆAˆa‰DØˆHr7   ©rQ   r  r   rF  )
rD   r‰  rk  Úcondlistrß  râ  rR  rU  r   r  s
   &&&       r5   r¥   Úkappa4_gen._get_support�  sü   € Ü—N’N 1 q¡5¨!¨a©%Ó0Ü—N’N 1 q¡5¨!¨q©&Ó1Ü—N’N 1 q¡5¨!¨a©%Ó0Ü—N’N 1¨¡6¨1¨q©5Ó1Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1¨q©5Ó1ð3ˆò	3ò	ò	ò
	ô ˜Ø "¨"Ð1Ø˜Ü!#§¡ô)ˆò
	ò	ô
 ˜Ø "¨"Ð1Ø˜Ü!#§¡ô)ˆð ˆvˆr7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  ©rD   rt   r‰  rk  s   &&&&r5   ru   Úkappa4_gen._pdf¸  r�  r7   c                ó@  € \         P                  ! V^ 8g  V^ 8g  4      \         P                  ! V^ 8H  V^ 8g  4      \         P                  ! V^ 8g  V^ 8H  4      \         P                  ! V^ 8H  V^ 8H  4      .pR pR pR pR p\        VWVWx.WV.\         P                  R7      # )r   c                óö   € \         P                  ! RV,          R,
          V) V ,          4      \         P                  ! RV,          R,
          V) RW ,          ,
          RV,          ,          ,          4      ,           # )zbpdf = (1.0 - k*x)**(1.0/k - 1.0)*(
       1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h-1.0)
logpdf = ...
r–   rÐ  ©rt   r‰  rk  s   &&&r5   rß  Úkappa4_gen._logpdf.<locals>.f0Ã  sX   € ô
 —J’J˜s 1�u s�{¨Q¨B¨q­DÓ1Ü—J’J˜s 1�u s�{¨Q¨B°°aµcµ	¸SÀ½UÕ/CÕ,CÓDõEð Fr7   c                ó    € \         P                  ! RV,          R,
          V) V ,          4      RW ,          ,
          RV,          ,          ,
          # )zTpdf = (1.0 - k*x)**(1.0/k - 1.0)*np.exp(-(
       1.0 - k*x)**(1.0/k))
logpdf = ...
r–   rÐ  rd  s   &&&r5   râ  Úkappa4_gen._logpdf.<locals>.f1Ë  s7   € ô
 —:’:˜c !�e c�k¨A¨2¨a­4Ó0°C¸!½#µIÀÀQÅÕ3GÕGÐGr7   c                ó–   € V ) \         P                  ! RV,          R,
          V) \        P                  ! V ) 4      ,          4      ,           # )zBpdf = np.exp(-x)*(1.0 - h*np.exp(-x))**(1.0/h - 1.0)
logpdf = ...
r–   )r|   r´  rQ   rÓ   rd  s   &&&r5   Úf2Úkappa4_gen._logpdf.<locals>.f2Ò  s4   € ð �2œŸ
š
 3 q¥5¨3¥;°°´2·6²6¸1¸"³:µÓ>Õ>Ð>r7   c                ó@   € V ) \         P                  ! V ) 4      ,
          # )z)pdf = np.exp(-x-np.exp(-x))
logpdf = ...
r7  rd  s   &&&r5   rR  Úkappa4_gen._logpdf.<locals>.f3Ø  s   € ð �2œŸš ˜r›
•?Ð"r7   rX  r\  ©	rD   rt   r‰  rk  r]  rß  râ  ri  rR  s	   &&&&     r5   rý   Úkappa4_gen._logpdf½  sž   € Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2ð4ˆò
	Fò	Hò	?ò	#ô ˜8Ø BÐ+Ø !˜9Ü#%§6¡6ô+ð 	+r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r  r`  s   &&&&r5   ry   Úkappa4_gen._cdfã  rÌ  r7   c                ó@  € \         P                  ! V^ 8g  V^ 8g  4      \         P                  ! V^ 8H  V^ 8g  4      \         P                  ! V^ 8g  V^ 8H  4      \         P                  ! V^ 8H  V^ 8H  4      .pR pR pR pR p\        VWVWx.WV.\         P                  R7      # )r   c                ó�   € RV,          \         P                  ! V) RW ,          ,
          RV,          ,          ,          4      ,          # )z;cdf = (1.0 - h*(1.0 - k*x)**(1.0/k))**(1.0/h)
logcdf = ...
r–   r_  rd  s   &&&r5   rß  Úkappa4_gen._logcdf.<locals>.f0ì  s2   € ð ˜•Eœ2Ÿ8š8 Q B¨¨a­c­	°S¸µUÕ';Õ$;Ó<Õ<Ð<r7   c                ó>   € RW ,          ,
          RV,          ,          ) # )z1cdf = np.exp(-(1.0 - k*x)**(1.0/k))
logcdf = ...
r–   r‹   rd  s   &&&r5   râ  Úkappa4_gen._logcdf.<locals>.f1ò  s   € ð ˜1�3•Y # a¥%Õ(Ð(Ð(r7   c                ó„   € RV,          \         P                  ! V) \        P                  ! V ) 4      ,          4      ,          # )z1cdf = (1.0 - h*np.exp(-x))**(1.0/h)
logcdf = ...
r–   )r|   ré  rQ   rÓ   rd  s   &&&r5   ri  Úkappa4_gen._logcdf.<locals>.f2ø  s,   € ð ˜•Eœ2Ÿ8š8 Q B¤r§v¢v¨q¨b£z¥MÓ2Õ2Ð2r7   c                ó2   € \         P                  ! V ) 4      ) # )z'cdf = np.exp(-np.exp(-x))
logcdf = ...
r7  rd  s   &&&r5   rR  Úkappa4_gen._logcdf.<locals>.f3þ  s   € ô —F’F˜A˜2“J�;Ðr7   rX  r\  rm  s	   &&&&     r5   r  Úkappa4_gen._logcdfæ  sœ   € Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2ð4ˆò
	=ò	)ò	3ò	ô ˜8Ø BÐ+Ø !˜9Ü#%§6¡6ô+ð 	+r7   c                ó@  € \         P                  ! V^ 8g  V^ 8g  4      \         P                  ! V^ 8H  V^ 8g  4      \         P                  ! V^ 8g  V^ 8H  4      \         P                  ! V^ 8H  V^ 8H  4      .pR pR pR pR p\        VWVWx.WV.\         P                  R7      # )r   c                 óf   € R V,          R R W,          ,
          V,          V,          ,
          ,          # r8  r‹   ©rƒ   r‰  rk  s   &&&r5   rß  Úkappa4_gen._ppf.<locals>.f0  s&   € Ø�q•5˜# #¨­¥,°Õ!1°AÕ 5Õ5Õ6Ð6r7   c                 óh   € R V,          R \         P                  ! V 4      ) V,          ,
          ,          # r8  rc  r}  s   &&&r5   râ  Úkappa4_gen._ppf.<locals>.f1  s$   € Ø�q•5˜#¤"§&¢&¨£) ¨a¥Õ/Õ0Ð0r7   c                ót   € \         P                  ! W,          ) 4      ) \        P                  ! V4      ,           # )z,ppf = -np.log((1.0 - (q**h))/h)
            r¤  r}  s   &&&r5   ri  Úkappa4_gen._ppf.<locals>.f2  s'   € ô —H’H˜q�t˜WÓ%Ð%¬¯ª¨q«	Õ1Ð1r7   c                 óZ   € \         P                  ! \         P                  ! V 4      ) 4      ) # rO   rc  r}  s   &&&r5   rR  Úkappa4_gen._ppf.<locals>.f3  s   € Ü—F’FœBŸFšF 1›I˜:Ó&Ð&Ð&r7   rX  r\  )	rD   rƒ   r‰  rk  r]  rß  râ  ri  rR  s	   &&&&     r5   r„   Úkappa4_gen._ppf	  sœ   € Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2Ü—N’N 1¨¡6¨1°©6Ó2ð4ˆò
	7ò	1ò	2ò
	'ô ˜8Ø BÐ+Ø !˜9Ü#%§6¡6ô+ð 	+r7   c                ót   € \         P                  ! V^ 8  V^ 8¬  4      V^ 8  .pR pR p\        W4V.W.^R7      # )r   c                 óH   € RV ,          V,          P                  \        4      # rš  ©Úastyper+  rI  s   &&r5   rß  Ú&kappa4_gen._get_stats_info.<locals>.f0(  s   € Ø˜•F˜1•H×$Ñ$¤SÓ)Ð)r7   c                 ó:   € RV,          P                  \        4      # rš  rˆ  rI  s   &&r5   râ  Ú&kappa4_gen._get_stats_info.<locals>.f1+  s   € Ø˜•F—?‘?¤3Ó'Ð'r7   rX  )rQ   r  r   )rD   r‰  rk  r]  rß  râ  s   &&&   r5   Ú_get_stats_infoÚkappa4_gen._get_stats_info"  sG   € ä�NŠN˜1˜q™5 ! q¡&Ó)Ø�‰Eð
ˆò
	*ò	(ô ˜8¨" X°¨v¸qÔAÐAr7   c                óÒ   € V P                  W4      p\        ^^4       Uu. uF3  p\        P                  ! WC8  4      '       d   RM\        P                  NK5  	  ppVR,          # u upi ©rM   NrO  )r�  rR  rQ   ræ  rF  )rD   r‰  rk  ÚmaxrrI  Úoutputss   &&&   r5   r   Úkappa4_gen._stats0  sU   € Ø×#Ñ# AÓ)ˆÜAFÀqÈ!ÄÓMÁ¸Aœ2Ÿ6š6 !¡(×+Ò+‘4´·±Ò7ÁˆÐMØ�q�zÐùò Ns    9A$c                óÔ   € V P                  V^ ,          V^,          4      pW8¼  d   \        P                  # \        P                  ! V P
                  ^ ^V3V,           R7      ^ ,          # ©r   r…  )r�  rQ   rF  r   r,  Ú_mom_integ1)rD   rì  rF   r‘  s   &&* r5   Ú_mom1_scÚkappa4_gen._mom1_sc5  sP   € Ø×#Ñ# D¨¥G¨T°!­WÓ5ˆØŒ9Ü—6‘6ˆMÜ�~Š~˜d×.Ñ.°°1¸A¸4À½9ÔEÀaÕHÐHr7   r‹   N)rŒ   r�   rŽ   r�   r�   rd   rm   r¥   ru   rý   ry   r  r„   r�  r   r—  r‘   r’   r“   s   @r5   r@  r@  -  sN   ø‡ € ñWòp/òò
'òR-ò
$+òL-ò!+òF+ò2Bò÷
Ið Ir7   r@  Úkappa4c                   ó`   a a€ ] tR tRt oRtR tR tR tV 3R ltR t	R t
R	 tR
 tRtVtV ;t# )Ú
kappa3_geni?  aÚ  Kappa 3 parameter distribution.

%(before_notes)s

Notes
-----
The probability density function for `kappa3` is:

.. math::

    f(x, a) = a (a + x^a)^{-(a + 1)/a}

for :math:`x > 0` and :math:`a > 0`.

`kappa3` takes ``a`` as a shape parameter for :math:`a`.

References
----------
P.W. Mielke and E.S. Johnson, "Three-Parameter Kappa Distribution Maximum
Likelihood and Likelihood Ratio Tests", Methods in Weather Research,
701-707, (September, 1973),
:doi:`10.1175/1520-0493(1973)101<0701:TKDMLE>2.3.CO;2`

B. Kumphon, "Maximum Entropy and Maximum Likelihood Estimation for the
Three-Parameter Kappa Distribution", Open Journal of Statistics, vol 2,
415-419 (2012), :doi:`10.4236/ojs.2012.24050`

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r3  rj   rl   s   &r5   rm   Úkappa3_gen._shape_info`  r6  r7   c                óV   € W"W,          ,           RV,          ^,
          ,          ,          # rš  r‹   r9  s   &&&r5   ru   Úkappa3_gen._pdfc  s   € à�a•d•(˜d 1�f Q�hÕ'Õ'Ð'r7   c                óH   € WW,          ,           RV,          ,          ,          # rš  r‹   r9  s   &&&r5   ry   Úkappa3_gen._cdfg  s   € Ø�a•d•(˜d 1�fÕ%Õ%Ð%r7   c           	     óH  <€ \         P                  ! W4      w  r\        SV `  W4      pR pW48  p\        P
                  ! \        P                  ! RW%,          ,          W%,          W,          W%,          ) ,          ,          4      4      ) pWd8„  pW5,          V,          Wg&   WcV&   V# )g{®Gáz„?r›  )rQ   rE  r@   r~   r|   rf  r´  )	rD   rt   r˜   ÚsfÚcutoffrS  Úsf2Úi2rØ  s	   &&&     €r5   r~   Úkappa3_gen._sfj  s„   ø€ Ü×"Ò" 1Ó(‰ˆÜ‰W‰[˜Óˆð
 ˆØ‰KˆÜ�xŠxœŸ
š
 4¨!­$¥;°µ°qµt¸a½d¸Uµ{Õ0BÓCÓDÐDˆØ‰\ˆØ•%˜•)ˆ‰àˆ1‰Øˆ	r7   c                óL   € W!V) ,          R ,
          ,          R V,          ,          # r8  r‹   rA  s   &&&r5   r„   Úkappa3_gen._ppfz  s   € Ø�q�b•5˜3•;• 3 q¥5Õ)Ð)r7   c                óŒ   € \         P                  ! V) V) 4      p\         P                  ! V4      pW$,          R V,          ,          # r8  rŸ  )rD   rƒ   r˜   Úlgr	  s   &&&  r5   rˆ   Úkappa3_gen._isf}  s4   € Ü�ZŠZ˜˜˜Q˜BÓˆÜ—’˜“ˆØ•	˜S 1�WÕ%Ð%r7   c                ó°   € \        ^^4       Uu. uF3  p\        P                  ! W!8  4      '       d   RM\        P                  NK5  	  ppVR,          # u upi r�  )rR  rQ   ræ  rF  )rD   r˜   rS  r’  s   &&  r5   r   Úkappa3_gen._stats‚  sC   € Ü>CÀAÀq¼kÓJ¹k¸œ2Ÿ6š6 !¡%Ÿ=š=‘4¬b¯f©fÒ4¹kˆÐJØ�q�zÐùò Ks   �9Ac                óÒ   € \         P                  ! W^ ,          8¬  4      '       d   \         P                  # \        P                  ! V P
                  ^ ^V3V,           R7      ^ ,          # r•  )rQ   ræ  rF  r   r,  r–  )rD   rì  rF   s   &&*r5   r—  Úkappa3_gen._mom1_sc†  sF   € Ü�6Š6�!˜A•w‘,×ÒÜ—6‘6ˆMÜ�~Š~˜d×.Ñ.°°1¸A¸4À½9ÔEÀaÕHÐHr7   r‹   )rŒ   r�   rŽ   r�   r�   rm   ru   ry   r~   r„   rˆ   r   r—  r‘   r’   r  r   s   @@r5   r›  r›  ?  s;   ù‡ € ñò@Eò(ò&õò *ò&ò
÷Iò Ir7   r›  Úkappa3c                   óX   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tRtV tR# )Ú	moyal_geni�  aS  A Moyal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `moyal` is:

.. math::

    f(x) = \exp(-(x + \exp(-x))/2) / \sqrt{2\pi}

for a real number :math:`x`.

%(after_notes)s

This distribution has utility in high-energy physics and radiation
detection. It describes the energy loss of a charged relativistic
particle due to ionization of the medium [1]_. It also provides an
approximation for the Landau distribution. For an in depth description
see [2]_. For additional description, see [3]_.

References
----------
.. [1] J.E. Moyal, "XXX. Theory of ionization fluctuations",
       The London, Edinburgh, and Dublin Philosophical Magazine
       and Journal of Science, vol 46, 263-280, (1955).
       :doi:`10.1080/14786440308521076` (gated)
.. [2] G. Cordeiro et al., "The beta Moyal: A useful skew distribution",
       International Journal of Research and Reviews in Applied Sciences,
       vol 10, 171-192, (2012).
       https://www.arpapress.com/files/volumes/vol10issue2/ijrras_10_2_02.pdf
.. [3] C. Walck, "Handbook on Statistical Distributions for
       Experimentalists; International Report SUF-PFY/96-01", Chapter 26,
       University of Stockholm: Stockholm, Sweden, (2007).
       http://www.stat.rice.edu/~dobelman/textfiles/DistributionsHandbook.pdf

.. versionadded:: 1.1.0

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úmoyal_gen._shape_infoº  r¼   r7   Nc                ób   € \         P                  R ^VVR7      p\        P                  ! V4      ) # )r£   )r˜   r.   rô   rõ   )r(  r)  rQ   r  )rD   rô   rõ   r*  s   &&& r5   rö   Úmoyal_gen._rvs½  s.   € Ü�Y‰Y˜ A¨DØ$0ð ó 2ˆä—’�r“
ˆ{Ðr7   c                óÔ   € \         P                  ! RV\         P                  ! V) 4      ,           ,          4      \         P                  ! ^\         P                  ,          4      ,          # ©r£   r#  )rQ   rÓ   r'  r  r¿   s   &&r5   ru   Úmoyal_gen._pdfÂ  s:   € Ü�vŠv�d˜a¤"§&¢&¨!¨£*�nÕ-Ó.´·²¸¼2¿5¹5½Ó1AÕAÐAr7   c                óš   € \         P                  ! \        P                  ! RV,          4      \        P                  ! ^4      ,          4      # r¹  )r|   r
  rQ   rÓ   r'  r¿   s   &&r5   ry   Úmoyal_gen._cdfÅ  s+   € Ü�wŠw”r—v’v˜d Q�hÓ'¬"¯'ª'°!«*Õ4Ó5Ð5r7   c                óš   € \         P                  ! \        P                  ! RV,          4      \        P                  ! ^4      ,          4      # r¹  )r|   r  rQ   rÓ   r'  r¿   s   &&r5   r~   Úmoyal_gen._sfÈ  s+   € Ü�vŠv”b—f’f˜T A�XÓ&¬¯ª°«Õ3Ó4Ð4r7   c                ót   € \         P                  ! ^\        P                  ! V4      ^,          ,          4      ) # rD  )rQ   r  r|   Úerfcinvr¿   s   &&r5   r„   Úmoyal_gen._ppfË  s&   € Ü—’�qœ2Ÿ:š: a›=¨!Õ+Õ+Ó,Ð,Ð,r7   c                óH  € \         P                  ! ^4      \         P                  ,           p\         P                  ^,          ^,          p^\         P                  ! ^4      ,          \
        P                  ! ^4      ,          \         P                  ^,          ,          pRpWW43# )rÑ   r¬  )rQ   r  Úeuler_gammar  r'  r|   r¸  rx  s   &    r5   r   Úmoyal_gen._statsÎ  sc   € Ü�VŠV�A‹YœŸ™Õ'ˆÜ�e‰e�Q�h˜�lˆØ”"—'’'˜!“*�_œrŸwšw q›zÕ)¬B¯E©E°1­HÕ4ˆØˆØ˜ˆÐr7   c                óÔ  € VR 8X  d,   \         P                  ! ^4      \         P                  ,           # VR8X  dV   \         P                  ^,          ^,          \         P                  ! ^4      \         P                  ,           ^,          ,           # VR8X  d­   R\         P                  ^,          ,          \         P                  ! ^4      \         P                  ,           ,          p\         P                  ! ^4      \         P                  ,           ^,          p^\        P
                  ! ^4      ,          pW#,           V,           # VR8X  Ed   ^8\        P
                  ! ^4      ,          \         P                  ! ^4      \         P                  ,           ,          p^\         P                  ^,          ,          \         P                  ! ^4      \         P                  ,           ^,          ,          p\         P                  ! ^4      \         P                  ,           ^,          p^\         P                  ^,          ,          ^,          pW#,           V,           V,           # V P                  V4      # )r–   rÒ   r£  rS  r¬  )rQ   r  rÃ  r  r|   r¸  r—  )rD   rc   Útmp1rú  Útmp3Útmp4s   &&    r5   r,  Úmoyal_gen._munpÕ  sj  € Ø�Œ8Ü—6’6˜!“9œrŸ~™~Õ-Ð-Ø�#ŒXÜ—5‘5˜!•8˜a•<¤2§6¢6¨!£9¬r¯~©~Õ#=ÀÕ"AÕAÐAØ�#ŒXØœŸ™ �•>¤R§V¢V¨A£Y¬r¯~©~Õ%=Õ>ˆDÜ—F’F˜1“IœbŸn™nÕ,¨qÕ0ˆDØœŸš ›
•?ˆDØ•; Õ%Ð%Ø�#�XØœBŸGšG A›JÕ&¬"¯&ª&°«)´b·n±nÕ*DÕEˆDØ”r—u‘u˜a•x•<¤2§6¢6¨!£9¬r¯~©~Õ#=ÀÕ"AÕAˆDÜ—F’F˜1“I¤§¡Õ.°Õ2ˆDØ”r—u‘u˜a•x•< !Õ#ˆDØ•; Õ%¨Õ,Ð,ð —=‘= Ó#Ð#r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   ry   r~   r„   r   r,  r‘   r’   r“   s   @r5   r³  r³  �  s9   ø‡ € ñ)òTôò
Bò6ò5ò-ò÷$ð $r7   r³  Úmoyalc                   ót   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tRR ltRR ltRtV tR# )Únakagami_geniî  a  A Nakagami continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `nakagami` is:

.. math::

    f(x, \nu) = \frac{2 \nu^\nu}{\Gamma(\nu)} x^{2\nu-1} \exp(-\nu x^2)

for :math:`x >= 0`, :math:`\nu > 0`. The distribution was introduced in
[2]_, see also [1]_ for further information.

`nakagami` takes ``nu`` as a shape parameter for :math:`\nu`.

%(after_notes)s

References
----------
.. [1] "Nakagami distribution", Wikipedia
       https://en.wikipedia.org/wiki/Nakagami_distribution
.. [2] M. Nakagami, "The m-distribution - A general formula of intensity
       distribution of rapid fading", Statistical methods in radio wave
       propagation, Pergamon Press, 1960, 3-36.
       :doi:`10.1016/B978-0-08-009306-2.50005-4`

%(example)s

c                ó   € V^ 8„  # r  r‹   )rD   Únus   &&r5   rd   Únakagami_gen._argcheck  s   € Ø�A‰vˆr7   c                ó@   € \        R R^ \        P                  3R4      .# )rÎ  Fr4  rj   rl   s   &r5   rm   Únakagami_gen._shape_info  r5  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  ©rD   rt   rÎ  s   &&&r5   ru   Únakagami_gen._pdf  r•  r7   c                ó  € \         P                  ! ^4      \        P                  ! W"4      ,           \        P                  ! V4      ,
          \        P                  ! ^V,          ^,
          V4      ,           W!^,          ,          ,
          # rD  )rQ   r  r|   rµ  r  rÓ  s   &&&r5   rý   Únakagami_gen._logpdf  sX   € ô —’�q“	œBŸHšH RÓ,Õ,¬r¯zªz¸"«~Õ=Ü—’˜˜2� � 1Ó%õ&Ø(*¨a­4­õ0ð 	1r7   c                óJ   € \         P                  ! W"V,          V,          4      # rO   rA  rÓ  s   &&&r5   ry   Únakagami_gen._cdf  s   € Ü�{Š{˜2 !�t A�vÓ&Ð&r7   c                ór   € \         P                  ! R V,          \        P                  ! W!4      ,          4      # r8  rJ  )rD   rƒ   rÎ  s   &&&r5   r„   Únakagami_gen._ppf   s#   € Ü�wŠw�s˜2•vœbŸnšn¨RÓ3Õ3Ó4Ð4r7   c                óJ   € \         P                  ! W"V,          V,          4      # rO   rE  rÓ  s   &&&r5   r~   Únakagami_gen._sf#  s   € Ü�|Š|˜B 1¥ Q¥Ó'Ð'r7   c                ór   € \         P                  ! ^V,          \        P                  ! W!4      ,          4      # r_   rO  )rD   rH  rÎ  s   &&&r5   rˆ   Únakagami_gen._isf&  s#   € Ü�wŠw�q˜•tœbŸošo¨bÓ4Õ4Ó5Ð5r7   c                óæ  € \         P                  ! VR 4      \        P                  ! V4      ,          pRW",          ,
          pV^^V,          V,          ,
          ,          R,          V,          \        P                  ! VR4      ,          pRV^,          ,          V,          ^V,          ^,
          V^,          ,          ,           ^V,          ,
          ^,           pWQVR,          ,          ,          pW#WE3# )r£   r–   rÒ   rS  éúÿÿÿ)r|   rT  rQ   r'  rU  )rD   rÎ  ry  rz  r{  r|  s   &&    r5   r   Únakagami_gen._stats)  s¨   € Ü�WŠW�R˜ÓœbŸgšg b›kÕ)ˆØ�"•%�iˆØ�1�q˜•t˜C•x•<Õ  3Õ&¨Õ+¬b¯hªh°s¸CÓ.@Õ@ˆØ��A•�X�b�[˜A˜b�D �F B¨¥E�>Õ)¨!¨B­$Õ.°Õ2ˆØ
��c•�kÕˆØ˜ˆÐr7   c                ó6  € \         P                  ! V4      p\         P                  ! V4      p\        P                  ! V4      pWR ,
          \        P
                  ! V4      ,          ,
          pR\         P                  ! V4      ,          \         P                  ! ^4      ,
          pW4,           V,           p\        P                  P                  4       pVR8„  pWX,          V,           ^^W,          ,          ,          ,
          Wh&   VP                  V4      R,          # )r£   g     jè@r#  r‹   )rQ   rG  ré  r|   r  rZ  r  rF  r/  r  r°  )	rD   rÎ  rG  rè  ré  r  r‰  Únorm_entropyrS  s	   &&       r5   r  Únakagami_gen._entropy1  s»   € Ü—’˜“ˆä�]Š]˜2ÓˆÜ�JŠJ�r‹NˆØ�s•(œbŸjšj¨›nÕ,Õ,ˆØ”2—6’6˜"“:Õ¤§¢ q£	Õ)ˆØ�E�A�Iˆä—z‘z×*Ñ*Ó,ˆð �‰Hˆà�t�lÕ" Q¨¨2­5­¥\Õ1ˆ‰Ø�y‰y˜Ó Õ#Ð#r7   Nc                ó\   € \         P                  ! VP                  WR 7      V,          4      # rà  )rQ   r'  r…  )rD   rÎ  rô   rõ   s   &&&&r5   rö   Únakagami_gen._rvsB  s$   € ä�wŠw�|×2Ñ2°2Ð2ÓAÀBÕFÓGÐGr7   c                óJ  € \        V\        4      '       d   VP                  4       pVf   RV P                  ,          p\        P
                  ! V4      p\        P                  ! \        P                  ! W,
          ^,          4      \        V4      ,          4      pW#V3,           # )Nr8  )	r>   r)   rÕ  ÚnumargsrQ   rR  r'  rè  rç  )rD   rE   rF   r-   r.   s   &&&  r5   r×  Únakagami_gen._fitstartF  sp   € Ü�dœL×)Ò)Ø—>‘>Ó#ˆDØŠ<Ø˜DŸL™LÕ(ˆDô �fŠf�T‹lˆÜ—’œŸš ¥
¨Q�Ó/´#°d³)Õ;Ó<ˆØ˜E�lÕ"Ð"r7   r‹   r.  rO   )rŒ   r�   rŽ   r�   r�   rd   rm   ru   rý   ry   r„   r~   rˆ   r   r  rö   r×  r‘   r’   r“   s   @r5   rÌ  rÌ  î  sM   ø‡ € ñò>òFò+ò1ò'ò5ò(ò6òò$ô"H÷	#ò 	#r7   rÌ  Únakagamic                 óš  € VR ,          R,
          p\         P                  ! V 4      \         P                  ! V4      rT\        P                  ! VR ,          W,          4      RWE,
          ^,          ,          ,
          p\        P                  ! W4V,          4      R ,          p\
        P                  ! V^ 8„  Wg3R \         P                  ) R7      # )rÒ   r–   r£   c                 ó<   € V \         P                  ! V4      ,           # rO   rc  )rI  r\  s   &&r5   r  Ú_ncx2_log_pdf.<locals>.<lambda>b  s   € �QœŸš ›–]r7   r  )rQ   r'  r|   rµ  Úiver  r  rk   )rt   r3  r³  Údf2r	  Únsr›  Úcorrs   &&&     r5   Ú_ncx2_log_pdfrò  V  sŽ   € ð ˆS�&�3�,€CÜ�WŠW�Q‹ZœŸš ›ˆÜ
�(Š(�3�s•7˜A�DÓ
! C¨­°1­Õ$4Õ
4€CÜ�6Š6�#˜"•uÓ Õ#€Dä�?Š?Øˆq‰Ø	ˆÙ"Ü—F‘F�7ô	ð r7   c                   ód   a € ] tR tRt o RtR tR tRR ltR tR t	R	 t
R
 tR tR tR tRtV tR# )Úncx2_genif  a¯  A non-central chi-squared continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `ncx2` is:

.. math::

    f(x, k, \lambda) = \frac{1}{2} \exp(-(\lambda+x)/2)
        (x/\lambda)^{(k-2)/4}  I_{(k-2)/2}(\sqrt{\lambda x})

for :math:`x >= 0`, :math:`k > 0` and :math:`\lambda \ge 0`.
:math:`k` specifies the degrees of freedom (denoted ``df`` in the
implementation) and :math:`\lambda` is the non-centrality parameter
(denoted ``nc`` in the implementation). :math:`I_\nu` denotes the
modified Bessel function of first order of degree :math:`\nu`
(`scipy.special.iv`).

`ncx2` takes ``df`` and ``nc`` as shape parameters.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
methods. [1]_

%(after_notes)s

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

%(example)s

c                óV   € V^ 8„  \         P                  ! V4      ,          V^ 8¬  ,          # r  rÅ  ©rD   r3  r³  s   &&&r5   rd   Úncx2_gen._argcheckŠ  s"   € Ø�Q‘œ"Ÿ+š+ b›/Õ)¨R°1©WÕ5Ð5r7   c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# )r3  Fr³  r4  ri   rj   ©rD   ÚidfÚincs   &  r5   rm   Úncx2_gen._shape_info�  s:   € Ü˜˜u q¬"¯&©& k°>ÓBˆÜ˜˜u q¬"¯&©& k°=ÓAˆØˆzÐr7   Nc                ó&   € VP                  WV4      # rO   )Únoncentral_chisquare)rD   r3  r³  rô   rõ   s   &&&&&r5   rö   Úncx2_gen._rvs’  s   € Ø×0Ñ0°¸Ó>Ð>r7   c                óH   € \         P                  ! V^ 8g  WV3\        R 4      # )r   c                 ó,   € \         P                  W4      # rO   )r7  rý   ©rt   r3  Ú_s   &&&r5   r  Ú"ncx2_gen._logpdf.<locals>.<lambda>—  s   € ´·±¸QÔ0Cr7   )r  r  rò  ©rD   rt   r3  r³  s   &&&&r5   rý   Úncx2_gen._logpdf•  s&   € Ü�Š˜r Q™w¨°¨´]ÙCóEð 	Er7   c                óØ   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! V^ 8g  WV3\        P
                  R 4      uuRRR4       #   + '       g   i     R# ; i)rl  r­  c                 ó,   € \         P                  W4      # rO   )r7  ru   r  s   &&&r5   r  Úncx2_gen._pdf.<locals>.<lambda>œ  ó   € ´D·I±I¸aÔ4Dr7   N)rQ   ro  r  r  rq   Ú	_ncx2_pdfr  s   &&&&r5   ru   Úncx2_gen._pdf™  óB   € Ü�[Š[˜h×'Ö'Ü—?’? 2¨¡7¨Q°B¨K¼¿¹Ù#DóF÷ (×'×'Ó'úó    -AÁA)	c                óØ   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! V^ 8g  WV3\        P
                  R 4      uuRRR4       #   + '       g   i     R# ; i)rl  r­  c                 ó,   € \         P                  W4      # rO   )r7  ry   r  s   &&&r5   r  Úncx2_gen._cdf.<locals>.<lambda>¡  r
  r7   N)rQ   ro  r  r  r|   Úchndtrr  s   &&&&r5   ry   Úncx2_gen._cdfž  sB   € Ü�[Š[˜h×'Ö'Ü—?’? 2¨¡7¨Q°B¨K¼¿¹Ù#DóF÷ (×'×'Ó'úr  c                óØ   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! V^ 8g  WV3\        P
                  R 4      uuRRR4       #   + '       g   i     R# ; i)rl  r­  c                 ó,   € \         P                  W4      # rO   )r7  r„   r  s   &&&r5   r  Úncx2_gen._ppf.<locals>.<lambda>¦  r
  r7   N)rQ   ro  r  r  r|   Úchndtrix©rD   rƒ   r3  r³  s   &&&&r5   r„   Úncx2_gen._ppf£  sB   € Ü�[Š[˜h×'Ö'Ü—?’? 2¨¡7¨Q°B¨K¼¿¹Ù#DóF÷ (×'×'Ó'úr  c                óØ   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! V^ 8g  WV3\        P
                  R 4      uuRRR4       #   + '       g   i     R# ; i)rl  r­  c                 ó,   € \         P                  W4      # rO   )r7  r~   r  s   &&&r5   r  Úncx2_gen._sf.<locals>.<lambda>«  s   € ´D·H±H¸Q´Or7   N)rQ   ro  r  r  rq   Ú_ncx2_sfr  s   &&&&r5   r~   Úncx2_gen._sf¨  sB   € Ü�[Š[˜h×'Ö'Ü—?’? 2¨¡7¨Q°B¨K¼¿¹Ù#CóE÷ (×'×'Ó'úr  c                óØ   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! V^ 8g  WV3\        P
                  R 4      uuRRR4       #   + '       g   i     R# ; i)rl  r­  c                 ó,   € \         P                  W4      # rO   )r7  rˆ   r  s   &&&r5   r  Úncx2_gen._isf.<locals>.<lambda>°  r
  r7   N)rQ   ro  r  r  rq   Ú	_ncx2_isfr  s   &&&&r5   rˆ   Úncx2_gen._isf­  r  r  c                ó(  € W,           pR  pRV! WR4      ,          p\         P                  ! R4      V! W^4      ,          \         P                  ! V! WR4      ^,          4      ,          pRV! WR4      ,          V! WR4      ^,          ,          pVVVV3# )c                 ó    € WV,          ,           # rO   r‹   )rk  r>  r\  s   &&&r5   Ú	k_plus_clÚ"ncx2_gen._stats.<locals>.k_plus_cl´  s   € Ø˜•s•7ˆNr7   rÒ   rþ  r�  r¬  rÇ  )rD   r3  r³  Ú
_ncx2_meanr&  Ú_ncx2_varianceÚ_ncx2_skewnessÚ_ncx2_kurtosis_excesss   &&&     r5   r   Úncx2_gen._stats²  s“   € Ø•Wˆ
ò	à¡	¨"°#Ó 6Õ6ˆÜŸ'š' #›,©°2¸1Ó)=Õ=ÜŸ'š'¡)¨B°CÓ"8¸!Õ";Ó<õ=ˆà!%©	°"¸#Ó(>Õ!>Ù!*¨2°3Ó!7¸Õ!:õ";Ðð ØØØ!ð	
ð 	
r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rd   rm   rö   rý   ru   ry   r„   r~   rˆ   r   r‘   r’   r“   s   @r5   rô  rô  f  sH   ø‡ € ñ"òF6òô
?òEòFò
Fò
Fò
Eò
F÷

ð 
r7   rô  Úncx2c                   ób   a € ] tR tRt o RtR tR tRR ltR tR t	R	 t
R
 tR tRR ltRtV tR# )Úncf_geniÆ  a¦  A non-central F distribution continuous random variable.

%(before_notes)s

See Also
--------
scipy.stats.f : Fisher distribution

Notes
-----
The probability density function for `ncf` is:

.. math::

    f(x, n_1, n_2, \lambda) =
        \exp\left(\frac{\lambda}{2} +
                  \lambda n_1 \frac{x}{2(n_1 x + n_2)}
            \right)
        n_1^{n_1/2} n_2^{n_2/2} x^{n_1/2 - 1} \\
        (n_2 + n_1 x)^{-(n_1 + n_2)/2}
        \gamma(n_1/2) \gamma(1 + n_2/2) \\
        \frac{L^{\frac{n_1}{2}-1}_{n_2/2}
            \left(-\lambda n_1 \frac{x}{2(n_1 x + n_2)}\right)}
        {B(n_1/2, n_2/2)
            \gamma\left(\frac{n_1 + n_2}{2}\right)}

for :math:`n_1, n_2 > 0`, :math:`\lambda \ge 0`.  Here :math:`n_1` is the
degrees of freedom in the numerator, :math:`n_2` the degrees of freedom in
the denominator, :math:`\lambda` the non-centrality parameter,
:math:`\gamma` is the logarithm of the Gamma function, :math:`L_n^k` is a
generalized Laguerre polynomial and :math:`B` is the beta function.

`ncf` takes ``dfn``, ``dfd`` and ``nc`` as shape parameters. If ``nc=0``,
the distribution becomes equivalent to the Fisher distribution.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``pdf``, ``cdf``, ``ppf``, ``stats``, ``sf`` and
``isf`` methods. [1]_

%(after_notes)s

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

%(example)s

c                ó4   € V^ 8„  V^ 8„  ,          V^ 8¬  ,          # r  r‹   )rD   rç  rè  r³  s   &&&&r5   rd   Úncf_gen._argcheck÷  s   € Ø�a‘˜C !™GÕ$¨¨a©Õ0Ð0r7   c                ó¾   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      p\        RR^ \        P                  3R4      pWV.# )rç  Frè  r³  r4  ri   rj   )rD   Úidf1Úidf2rû  s   &   r5   rm   Úncf_gen._shape_infoú  sU   € Ü˜% ¨¬B¯F©F¨°^ÓDˆÜ˜% ¨¬B¯F©F¨°^ÓDˆÜ˜˜u q¬"¯&©& k°=ÓAˆØ˜CÐ Ð r7   Nc                ó&   € VP                  WW44      # rO   )Únoncentral_f)rD   rç  rè  r³  rô   rõ   s   &&&&&&r5   rö   Úncf_gen._rvs   s   € Ø×(Ñ(¨°2Ó<Ð<r7   c                ó0   € \         P                  ! WW44      # rO   )rq   Ú_ncf_pdf©rD   rt   rç  rè  r³  s   &&&&&r5   ru   Úncf_gen._pdf  s   € Ü�|Š|˜A CÓ,Ð,r7   c                ó0   € \         P                  ! W#WA4      # rO   )r|   Úncfdtrr;  s   &&&&&r5   ry   Úncf_gen._cdf  s   € Ü�yŠy˜ 2Ó)Ð)r7   c                ó¬   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! W#WA4      uuRRR4       #   + '       g   i     R# ; ir¬  )rQ   ro  r|   Úncfdtri)rD   rƒ   rç  rè  r³  s   &&&&&r5   r„   Úncf_gen._ppf	  s.   € Ü�[Š[˜h×'Ö'Ü—:’:˜c¨Ó.÷ (×'×'Ó'úr²  c                ó0   € \         P                  ! WW44      # rO   )rq   Ú_ncf_sfr;  s   &&&&&r5   r~   Úncf_gen._sf  s   € Ü�{Š{˜1 3Ó+Ð+r7   c                ó¬   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! WW44      uuRRR4       #   + '       g   i     R# ; ir¬  )rQ   ro  rq   Ú_ncf_isfr;  s   &&&&&r5   rˆ   Úncf_gen._isf  s.   € Ü�[Š[˜h×'Ö'Ü—<’< ¨Ó0÷ (×'×'Ó'úr²  c                óô   € \         P                  ! WV4      p\         P                  ! WV4      pR V9   d   \         P                  ! WV4      MRpRV9   d   \         P                  ! WV4      ^,
          MRpWVWx3# ©rj  Nrk  )rq   Ú	_ncf_meanÚ_ncf_varianceÚ_ncf_skewnessÚ_ncf_kurtosis_excess)	rD   rç  rè  r³  rl  ry  rz  r{  r|  s	   &&&&&    r5   r   Úncf_gen._stats  sv   € Ü�]Š]˜3 RÓ(ˆÜ×Ò ¨"Ó-ˆØ03°w´ŒS×Ò˜s¨Ô,ÀDˆà!$¨¤ô ×%Ò%Ø�bóØöØ59ð 	ð ˜ˆÐr7   r‹   r.  rq  ©rŒ   r�   rŽ   r�   r�   rd   rm   rö   ru   ry   r„   r~   rˆ   r   r‘   r’   r“   s   @r5   r/  r/  Æ  s=   ø‡ € ñ/ò`1ò!ô=ò-ò*ò/ò,ò1÷ò r7   r/  Úncfc                   ód   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 tR tR tR tRtV tR# )Út_geni)  a?  A Student's t continuous random variable.

For the noncentral t distribution, see `nct`.

%(before_notes)s

See Also
--------
nct

Notes
-----
The probability density function for `t` is:

.. math::

    f(x, \nu) = \frac{\Gamma((\nu+1)/2)}
                    {\sqrt{\pi \nu} \Gamma(\nu/2)}
                (1+x^2/\nu)^{-(\nu+1)/2}

where :math:`x` is a real number and the degrees of freedom parameter
:math:`\nu` (denoted ``df`` in the implementation) satisfies
:math:`\nu > 0`. :math:`\Gamma` is the gamma function
(`scipy.special.gamma`).

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r2  rj   rl   s   &r5   rm   Út_gen._shape_infoH  r5  r7   Nc                ó&   € VP                  WR 7      # rà  )Ú
standard_tr8  s   &&&&r5   rö   Ú
t_gen._rvsK  s   € Ø×&Ñ& rÐ&Ó5Ð5r7   c                ód   a € \         P                  ! V\        P                  8H  W3R  V 3R l4      # )c                 ó,   € \         P                  V 4      # rO   )r/  ru   ©rt   r3  s   &&r5   r  Út_gen._pdf.<locals>.<lambda>Q  s   € œ$Ÿ)™) Aœ,r7   c                 óN   <€ \         P                  ! SP                  W4      4      # rO   r.  )rt   r3  rD   s   &&€r5   r  r\  R  s   ø€ œ"Ÿ&š& §¡¨aÓ!4Ô5r7   rU  r;  s   f&&r5   ru   Ú
t_gen._pdfN  s)   ø€ Ü�ŠØ”"—&‘&‰L˜1˜'Ù&Ü5ó7ð 	7r7   c                ób   € R  pR p\         P                  ! V\        P                  8H  W3WC4      # )c                 óv  € \         P                  ! \        P                  ! R V,          R 4      4      R \         P                  ! V4      \         P                  ! \         P                  4      ,           ,          ,
          V^,           ^,          \         P
                  ! W ,          V,          4      ,          ,
          # r  )rQ   r  r|   rT  r  ré  r[  s   &&r5   Út_logpdfÚt_gen._logpdf.<locals>.t_logpdfV  sl   € Ü—F’Fœ2Ÿ7š7 3¨¥8¨SÓ1Ó2ØœRŸVšV B›Z¬"¯&ª&´·±«-Õ7Õ8õ9à˜A•v˜q•j¤§¢¨!­%°­(Ó!3Õ3õ4ð 5r7   c                 ó,   € \         P                  V 4      # rO   )r/  rý   r[  s   &&r5   Únorm_logpdfÚ"t_gen._logpdf.<locals>.norm_logpdf[  s   € Ü—<‘< “?Ð"r7   rU  )rD   rt   r3  ra  rd  s   &&&  r5   rý   Út_gen._logpdfT  s+   € ò	5ò
	#ô �Š˜r¤R§V¡V™|¨a¨W°kÓLÐLr7   c                ó.   € \         P                  ! W!4      # rO   ©r|   Ústdtrr;  s   &&&r5   ry   Ú
t_gen._cdf`  rt  r7   c                ó0   € \         P                  ! W!) 4      # rO   rh  r;  s   &&&r5   r~   Ú	t_gen._sfc  s   € Ü�xŠx˜˜BÓÐr7   c                ó.   € \         P                  ! W!4      # rO   ©r|   ÚstdtritrL  s   &&&r5   r„   Ú
t_gen._ppff  s   € Ü�zŠz˜"Ó Ð r7   c                ó0   € \         P                  ! W!4      ) # rO   rn  rL  s   &&&r5   rˆ   Ú
t_gen._isfi  s   € Ü—
’
˜2Ó!Ð!Ð!r7   c                ó*  € \         P                  ! V4      p\         P                  ! V^8„  R\         P                  4      pV^8„  V^8*  ,          V^8„  \         P                  ! V4      ,          V3pR R R 3p\        WEV3\         P                  4      p\         P                  ! V^8„  R\         P                  4      pV^8„  V^8*  ,          V^8„  \         P                  ! V4      ,          V3pR R R 3p\        WEV3\         P                  4      pW6Wx3# )rM   r•   c                 ó`   € \         P                  ! \         P                  V P                  4      # rO   ©rQ   Úbroadcast_tork   rG  r[  s   &r5   r  Út_gen._stats.<locals>.<lambda>u  ó   € ¤§¢´·±¸¿¹Ô!Br7   c                 ó    € W R ,
          ,          # rr  r‹   r[  s   &r5   r  rw  v  s
   €  ¨#¥v¦r7   c                 óD   € \         P                  ! ^V P                  4      # r_   ©rQ   rv  rG  r[  s   &r5   r  rw  w  ó   € ¤§¢°°B·H±HÔ!=r7   c                 ó`   € \         P                  ! \         P                  V P                  4      # rO   ru  r[  s   &r5   r  rw    rx  r7   c                 ó"   € R V R,
          ,          # )rJ  r¬  r‹   r[  s   &r5   r  rw  €  s   €  ¨¨3­¦r7   c                 óD   € \         P                  ! ^ V P                  4      # r  r{  r[  s   &r5   r  rw  �  r|  r7   )rQ   Úisposinfr±  rk   r$  r   rF  )	rD   r3  Úinfinite_dfry  r]  Ú
choicelistrz  r{  r|  s	   &&       r5   r   Út_gen._statsl  sû   € ä—k’k "“oˆä�XŠX�b˜1‘f˜c¤2§6¡6Ó*ˆà˜!‘V  a¡Õ(Ø˜!‘VœrŸ{š{¨2›Õ.Øð!ˆñ CÙ.Ù=ð?ˆ
ô ˜(°°´r·v±vÓ>ˆä�XŠX�b˜1‘f˜c¤2§6¡6Ó*ˆà˜!‘V  a¡Õ(Ø˜!‘VœrŸ{š{¨2›Õ.Øð!ˆñ CÙ/Ù=ð?ˆ
ô ˜°¨u´b·f±fÓ=ˆà˜ˆÐr7   c                ó–   € V\         P                  8X  d   \        P                  4       # R  pR p\        P
                  ! V^d8¬  WV4      # )c                 ó:  € V ^,          pV ^,           ^,          pV\         P                  ! V4      \         P                  ! V4      ,
          ,          \        P                  ! \        P                  ! V 4      \         P
                  ! VR4      ,          4      ,           # rI  )r|   rZ  rQ   r  r'  r©  )r3  ÚhalfÚhalf1s   &  r5   ró  Út_gen._entropy.<locals>.regularŠ  se   € Ø�a•4ˆDØ˜!•V˜Q•JˆEØœ2Ÿ:š: eÓ,¬r¯zªz¸$Ó/?Õ?Õ@Ü—f’fœRŸWšW R›[¬¯ª°°sÓ);Õ;Ó<õ=ð >r7   c                 ó  € \         P                  4       ^V ,          ,           V R,          ^,          ,           V R,          ^,          ,
          V R,          ^,          ,
          RV R,          ,          ,           V R,          ^,          ,           pV# )rM   rö  r÷  rø  g333333Ó?r  r  )r/  r  )r3  r‰  s   & r5   rì  Ú"t_gen._entropy.<locals>.asymptotic�  sg   € ô —‘“ 1 R¥4Õ'¨2¨s­7°A­+Õ5¸¸S½À!½ÕCØ˜•G˜Q•;õØ!% r¨3¥w¥õ0Ø35°sµ7¸Aµ+õ>ˆAàˆHr7   )rQ   rk   r/  r  r  r  )rD   r3  ró  rì  s   &&  r5   r  Út_gen._entropy†  s<   € Ø”—‘Œ<Ü—=‘=“?Ð"ò	>ò	ô �Š˜r S™y¨"¸'ÓBÐBr7   r‹   r.  rd  r“   s   @r5   rS  rS  )  sE   ø‡ € ñò<Fô6ò7ò
Mòò ò!ò"ò÷4Cð Cr7   rS  r±  c                   ób   a € ] tR tRt o RtR tR tRR ltR tR t	R	 t
R
 tR tRR ltRtV tR# )Únct_geniž  aE  A non-central Student's t continuous random variable.

%(before_notes)s

Notes
-----
If :math:`Y` is a standard normal random variable and :math:`V` is
an independent chi-square random variable (`chi2`) with :math:`k` degrees
of freedom, then

.. math::

    X = \frac{Y + c}{\sqrt{V/k}}

has a non-central Student's t distribution on the real line.
The degrees of freedom parameter :math:`k` (denoted ``df`` in the
implementation) satisfies :math:`k > 0` and the noncentrality parameter
:math:`c` (denoted ``nc`` in the implementation) is a real number.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``pdf``, ``cdf``, ``ppf``, ``sf`` and ``isf``
methods. [1]_

%(after_notes)s

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

%(example)s

c                ó   € V^ 8„  W"8H  ,          # r  r‹   rö  s   &&&r5   rd   Únct_gen._argcheck¿  s   € Ø�Q‘˜2™8Õ$Ð$r7   c                óž   € \        R R^ \        P                  3R4      p\        RR\        P                  ) \        P                  3R4      pW.# )r3  Fr³  r4  rj   rù  s   &  r5   rm   Únct_gen._shape_infoÂ  sA   € Ü˜˜u q¬"¯&©& k°>ÓBˆÜ˜˜u¬¯© w´·±Ð&7¸ÓHˆØˆzÐr7   Nc                óÎ   € \         P                  W#VR 7      p\        P                  WVR7      pV\        P                  ! V4      ,          \        P                  ! V4      ,          # )rÕ  r'  )r/  r)  r7  rQ   r'  )rD   r3  r³  rô   rõ   rc   rÇ  s   &&&&&  r5   rö   Únct_gen._rvsÇ  sE   € Ü�H‰H˜°\ˆHÓBˆÜ�X‰X�b°,ˆXÓ?ˆØ”2—7’7˜2“;�¤§¢¨£Õ,Ð,r7   c                ó0   € \         P                  ! WV4      # rO   )rq   Ú_nct_pdfr  s   &&&&r5   ru   Únct_gen._pdfÌ  s   € Ü�|Š|˜A 2Ó&Ð&r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Únctdtrr  s   &&&&r5   ry   Únct_gen._cdfÏ  s   € Ü�yŠy˜ Ó#Ð#r7   c                ó0   € \         P                  ! W#V4      # rO   )r|   Únctdtritr  s   &&&&r5   r„   Únct_gen._ppfÒ  s   € Ü�{Š{˜2 1Ó%Ð%r7   c           	     óØ   € \         P                  ! R R7      ;_uu_ 4        \         P                  ! \        P                  ! WV4      ^ ^4      uuRRR4       #   + '       g   i     R# ; ir¬  )rQ   ro  Úcliprq   Ú_nct_sfr  s   &&&&r5   r~   Únct_gen._sfÕ  s;   € Ü�[Š[˜h×'Ö'Ü—7’7œ3Ÿ;š; q¨bÓ1°1°aÓ8÷ (×'×'Ó'úr  c                ó¬   € \         P                  ! R R7      ;_uu_ 4        \        P                  ! WV4      uuRRR4       #   + '       g   i     R# ; ir¬  )rQ   ro  rq   Ú_nct_isfr  s   &&&&r5   rˆ   Únct_gen._isfÙ  s.   € Ü�[Š[˜h×'Ö'Ü—<’<  rÓ*÷ (×'×'Ó'úr²  c                óÞ   € \         P                  ! W4      p\         P                  ! W4      pR V9   d   \         P                  ! W4      MRpRV9   d   \         P                  ! W4      MRpWEWg3# rJ  )rq   Ú	_nct_meanÚ_nct_varianceÚ_nct_skewnessÚ_nct_kurtosis_excess)rD   r3  r³  rl  ry  rz  r{  r|  s   &&&&    r5   r   Únct_gen._statsÝ  sZ   € Ü�]Š]˜2Ó"ˆÜ×Ò Ó'ˆØ*-°¬.ŒS×Ò˜rÔ&¸dˆØ14¸´ŒS×%Ò% bÔ-ÀTˆØ˜ˆÐr7   r‹   r.  rq  rP  r“   s   @r5   r�  r�  ž  s=   ø‡ € ñò@%òô
-ò
'ò$ò&ò9ò+÷ò r7   r�  Únctc                   óŠ   a a€ ] tR tRt oRtR tR tR tR tR t	R t
RR	 ltR
 t]]! ]4      V 3R l4       4       tRtVtV ;t# )Ú
pareto_geniè  a   A Pareto continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `pareto` is:

.. math::

    f(x, b) = \frac{b}{x^{b+1}}

for :math:`x \ge 1`, :math:`b > 0`.

`pareto` takes ``b`` as a shape parameter for :math:`b`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r”  rj   rl   s   &r5   rm   Úpareto_gen._shape_infoþ  r6  r7   c                ó0   € W!V) ^,
          ,          ,          # r_   r‹   r—  s   &&&r5   ru   Úpareto_gen._pdf   s   € à˜�r˜!•t•9�}Ðr7   c                ó"   € ^W) ,          ,
          # r_   r‹   r—  s   &&&r5   ry   Úpareto_gen._cdf   s   € Ø�1�r•7�{Ðr7   c                ó6   € \        ^V,
          RV,          4      # )rM   r›  r:  r©  s   &&&r5   r„   Úpareto_gen._ppf   s   € Ü�1�Q•3˜˜Q�ÓÐr7   c                ó   € W) ,          # rO   r‹   r—  s   &&&r5   r~   Úpareto_gen._sf   s   € Ø�2�wˆr7   c                ó>   € \         P                  ! VRV,          4      # rš  rÆ  r©  s   &&&r5   rˆ   Úpareto_gen._isf   s   € Ü�xŠx˜˜4 !�8Ó$Ð$r7   c                ó<  € R
w  r4rVRV9   dz   V^8„  p\         P                  ! Wq4      p\         P                  ! \         P                  ! V4      \         P                  R7      p\         P
                  ! W7WˆR,
          ,          4       RV9   d�   V^8„  p\         P                  ! Wq4      p\         P                  ! \         P                  ! V4      \         P                  R7      p\         P
                  ! WGWˆR,
          ,          VR,
          ^,          ,          4       RV9   dÈ   V^8„  p\         P                  ! Wq4      p\         P                  ! \         P                  ! V4      \         P                  R7      p^VR,           ,          \         P                  ! VR,
          4      ,          VR,
          \         P                  ! V4      ,          ,          p	\         P
                  ! WWV	4       RV9   d«   V^8„  p\         P                  ! Wq4      p\         P                  ! \         P                  ! V4      \         P                  R7      pR	\         P                  ! . ROV4      ,          \         P                  ! . ROV4      ,          p	\         P
                  ! WgV	4       W4WV3# )Nrì  r  r–   r  rÒ   rj  r£  rk  rJ  rï  )r–   r–   rà  r<  )r–   g      Àr�  r•   )	rQ   ÚextractrB  rG  rk   ÚplacerF  r'  rØ
  )
rD   r™   rl  ry  rz  r{  r|  ÚmaskÚbtrm  s
   &&&       r5   r   Úpareto_gen._stats   s­  € Ø0‰ˆ�Ø�'Œ>Ø�q‘5ˆDÜ—’˜DÓ$ˆBÜ—’œŸš !›´·±Ô8ˆBÜ�HŠH�R˜r¨¥V�}Ô-Ø�'Œ>Ø�q‘5ˆDÜ—’˜DÓ$ˆBÜ—'’'œ"Ÿ(š( 1›+´"·&±&Ô9ˆCÜ�HŠH�S ¨¥f¥°°Cµ¸!µÕ ;Ô<Ø�'Œ>Ø�q‘5ˆDÜ—’˜DÓ$ˆBÜ—’œŸš !›´·±Ô8ˆBØ˜˜S�•>¤B§G¢G¨B°­HÓ$5Õ5¸"¸s½(ÄbÇgÂgÈbÃkÕ9QÕRˆDÜ�HŠH�R˜tÔ$Ø�'Œ>Ø�q‘5ˆDÜ—’˜DÓ$ˆBÜ—’œŸš !›´·±Ô8ˆBØœŸ
š
Ò#5°rÓ:Õ:Ü—J’JÒ5°rÓ:õ;ˆDä�HŠH�R˜tÔ$Ø˜ˆÐr7   c                óX   € ^RV,          ,           \         P                  ! V4      ,
          # r&  rc  ©rD   r™   s   &&r5   r  Úpareto_gen._entropy,   ó   € Ø�3�q•5�yœ2Ÿ6š6 !›9Õ$Ð$r7   c                óz  <aaaaaaa€ \        V SW#4      pVw  oorVVeI   \        P                  ! S4      V,
          T;'       g    ^ 8  d   \        R^\        P                  R7      hSP
                  ^ ,          oVV3R loYVu;J d   EfP   M EMKV3R loV3R loVVVVV3R loV3R lp\        VP                  R^4      4      pV^,          V^,          r©V! Wš4      '       g1   V	^ 8”  g   V
\        P                  8  d   V	^,          p	V
^,          p
K>  \        SWš.R	7      pVP                  '       d•   VP                  p\        P                  ! S4      V,
          pS;'       g	    S! WÍ4      pWÍ,           \        P                  ! S4      8  g5   \        P                  ! S4      V,
          p\        P                  ! V^ 4      pWíV3# \        SV `4  ! S3/ VB # Vf   \        P                  ! S4      V,
          pMTpT;'       g    \        P                  ! S4      V,
          pS;'       g	    S! WÍ4      pWíV3# )
NÚparetorÛ  c                 ó‚   <€ S\         P                  ! \         P                  ! SV,
          V ,          4      4      ,          # rO   rã
  )r.   ÚlocationrE   Úndatas   &&€€r5   Ú	get_shapeÚ!pareto_gen.fit.<locals>.get_shape<   s+   ø€ ð œ2Ÿ6š6¤"§&¢&¨$°­/¸UÕ)BÓ"CÓDÕDÐDr7   c                 ó$   <€ SV ,          V,          # rO   r‹   )rG  r.   rÇ  s   &&€r5   Ú	dL_dScaleÚ!pareto_gen.fit.<locals>.dL_dScaleG   s   ø€ ð ˜u•} uÕ,Ð,r7   c                 óh   <€ V ^,           \         P                  ! ^SV,
          ,          4      ,          # r_   r×  )rG  rÆ  rE   s   &&€r5   ÚdL_dLocationÚ$pareto_gen.fit.<locals>.dL_dLocationL   s&   ø€ ð  �	¤R§V¢V¨A°¸µÕ,AÓ%BÕBÐBr7   c                 óŒ   <€ \         P                  ! S4      V ,
          pS;'       g	    S! W4      pS! W!4      S! W 4      ,
          # rO   )rQ   rR  )r.   rÆ  rG  rÎ  rË  rE   rß
  rÈ  s   &  €€€€€r5   rÚ  Ú$pareto_gen.fit.<locals>.fun_to_solveQ   s>   ø€ ô Ÿ6š6 $›<¨%Õ/�Ø×<Ð<¡)¨EÓ"<�Ù# EÓ4±yÀÓ7NÕNÐNr7   c                 óv   <€ \         P                  ! S! V 4      4      \         P                  ! S! V4      4      8g  # rO   rP   ©rS   rT   rÚ  s   &&€r5   rU   Ú.pareto_gen.fit.<locals>.interval_contains_rootX   s/   ø€ äŸš¡¨VÓ 4Ó5ÜŸš¡¨VÓ 4Ó5ñ6ð 7r7   r.   rÜ  )rR  rQ   rR  rƒ  rk   rG  r  r<   r*   rî
  rS  rí
  r@   rB   )rD   rE   rF   r4   rï
  r  r  rU   rš  rS   rT   r›  r.   r-   rG  rÎ  rË  rß
  rÚ  rÈ  rÇ  rØ  s   &f*,           @@@@@@€r5   rB   Úpareto_gen.fit/   sÓ  ÿ€ ô 1°°t¸TÓHˆ
Ø%/Ñ"ˆˆf�dð Ò¤§¢ t£¨tÕ 3°v·{°{ÀÔ CÜ˜x¨q¼¿¹Ô?Ð?à—
‘
˜1•ˆö	Eð
 ×!Õ!õ-õ
C÷
Oñ Oõ7ô   §¡¨°!Ó 4Ó5ˆKØ(¨1�_¨k¸A­o�Fñ .¨f×=Ò=Ø œ
 f¬r¯v©v¤oØ˜!•�Ø˜!•’Ü˜l°VÐ4DÔEˆCØ�}�}ˆ}ØŸ™�Ü—f’f˜T“l UÕ*�Ø×7Ð7¡)¨EÓ"7�ð �¤r§v¢v¨d£|Ô3ÜŸFšF 4›L¨3Õ.�EÜŸLšL¨°Ó2�EØ 5Ð(Ð(ä‘w’{ 4Ñ0¨4Ñ0Ð0ØŠ\Ü—&’&˜“, Õ'‰CàˆCð ×,Ð,œ"Ÿ&š& ›,¨Õ,ˆØ×/Ð/™) EÓ/ˆØ˜5Ð Ð r7   r‹   rq  )rŒ   r�   rŽ   r�   r�   rm   ru   ry   r„   r~   rˆ   r   r  rK   r   r   rB   r‘   r’   r  r   s   @@r5   r¬  r¬  è  s\   ù‡ € ñò*Eòòò òò%ôò6%ð Ù˜MÓ*ôR!ó +ó ÷R!ð R!r7   r¬  rÄ  c                   ó`   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tRtV tR# )Ú	lomax_geni‰   aw  A Lomax (Pareto of the second kind) continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `lomax` is:

.. math::

    f(x, c) = \frac{c}{(1+x)^{c+1}}

for :math:`x \ge 0`, :math:`c > 0`.

`lomax` takes ``c`` as a shape parameter for :math:`c`.

`lomax` is a special case of `pareto` with ``loc=-1.0``.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úlomax_gen._shape_info¡   r6  r7   c                óL   € VR ,          R V,           VR ,           ,          ,          # r8  r‹   r`  s   &&&r5   ru   Úlomax_gen._pdf¤   s   € à��u�c˜!•e˜q �uÕ%Õ%Ð%r7   c                ó€   € \         P                  ! V4      V^,           \        P                  ! V4      ,          ,
          # r_   r©  r`  s   &&&r5   rý   Úlomax_gen._logpdf¨   s&   € Ü�vŠv�a‹y˜A˜a�C¤§¢¨!£Õ,Õ,Ð,r7   c                óh   € \         P                  ! V) \         P                  ! V4      ,          4      ) # rO   re  r`  s   &&&r5   ry   Úlomax_gen._cdf«   s"   € Ü—’˜!˜œBŸHšH Q›K�Ó(Ð(Ð(r7   c                óf   € \         P                  ! V) \        P                  ! V4      ,          4      # rO   )rQ   rÓ   r|   ré  r`  s   &&&r5   r~   Úlomax_gen._sf®   s   € Ü�vŠv�q�bœŸš !›•nÓ%Ð%r7   c                ó>   € V) \         P                  ! V4      ,          # rO   r_  r`  s   &&&r5   r
  Úlomax_gen._logsf±   s   € Øˆr”"—(’(˜1“+�~Ðr7   c                óh   € \         P                  ! \         P                  ! V) 4      ) V,          4      # rO   re  rg  s   &&&r5   r„   Úlomax_gen._ppf´   s!   € Ü�xŠxœŸš 1 "›˜ a�Ó(Ð(r7   c                ó0   € VRV,          ,          ^,
          # rš  r‹   rg  s   &&&r5   rˆ   Úlomax_gen._isf·   s   € Ø�4˜!•8�}˜qÕ Ð r7   c                ó@   € \         P                  VRRR7      w  r#rEW#WE3# )r–   rz  )r-   rl  r›  )rÄ  rF  r¹  s   &&    r5   r   Úlomax_gen._statsº   s$   € Ü Ÿ,™, q¨d¸F˜,ÓC‰ˆ�Ø˜ˆÐr7   c                óX   € ^RV,          ,           \         P                  ! V4      ,
          # r&  rc  r÷  s   &&r5   r  Úlomax_gen._entropy¾   s   € Ø��Q•�w”r—v’v˜a“yÕ Ð r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r~   r
  r„   rˆ   r   r  r‘   r’   r“   s   @r5   r×  r×  ‰   sB   ø‡ € ñò.Eò&ò-ò)ò&òò)ò!ò÷!ð !r7   r×  Úlomaxc                   óš   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 tRR ltR t]]! ]RR7      V 3R l4       4       tRtVtV ;t# )Úpearson3_geniÅ   a  A pearson type III continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `pearson3` is:

.. math::

    f(x, \kappa) = \frac{|\beta|}{\Gamma(\alpha)}
                   (\beta (x - \zeta))^{\alpha - 1}
                   \exp(-\beta (x - \zeta))

where:

.. math::

        \beta = \frac{2}{\kappa}

        \alpha = \beta^2 = \frac{4}{\kappa^2}

        \zeta = -\frac{\alpha}{\beta} = -\beta

:math:`\Gamma` is the gamma function (`scipy.special.gamma`).
Pass the skew :math:`\kappa` into `pearson3` as the shape parameter
``skew``.

%(after_notes)s

%(example)s

References
----------
R.W. Vogel and D.E. McMartin, "Probability Plot Goodness-of-Fit and
Skewness Estimation Procedures for the Pearson Type 3 Distribution", Water
Resources Research, Vol.27, 3149-3158 (1991).

L.R. Salvosa, "Tables of Pearson's Type III Function", Ann. Math. Statist.,
Vol.1, 191-198 (1930).

"Using Modern Computing Tools to Fit the Pearson Type III Distribution to
Aviation Loads Data", Office of Aviation Research (2003).

c                ó:  € R pRpRp\         P                  ! RW4      w  rapVP                  4       p\         P                  ! V4      V8  pV( pRW(,          V,          ,          p	WI,          ^,          p
W:V	,          ,
          pW‘V,          V,
          ,          pWaWÇW‰W«3# )r•   r–   g�íµ ÷Æð>rÒ   )rQ   rE  rÎ  r	  )rD   rt   rL  r-   r.   Únorm2pearson_transitionÚansr¼  Úinvmaskr©  rK  r¸  Útransxs   &&&          r5   Ú_preprocessÚpearson3_gen._preprocessó   s�   € ð
 ˆØˆð #+Ðä×*Ò*¨3°Ó8‰ˆ�Ø�h‰h‹jˆô �{Š{˜4Ó Ð#:Ñ:ˆØ�%ˆà�d•m eÕ+Õ,ˆØ• Õ!ˆØ˜T•\Õ!ˆà˜7� dÕ*Õ+ˆØ�v W°EÐ?Ð?r7   c                ó.   € \         P                  ! V4      # rO   rÅ  )rD   rL  s   &&r5   rd   Úpearson3_gen._argcheck!  s   € ô
 �{Š{˜4Ó Ð r7   c                ó^   € \        R R\        P                  ) \        P                  3R4      .# )rL  Fr4  rj   rl   s   &r5   rm   Úpearson3_gen._shape_info!  s%   € Ü˜6 5¬B¯F©F¨7´B·F±FÐ*;¸^ÓLÐMÐMr7   c                ó6   € R pRpTpRV^,          ,          pW#WE3# )r•   r–   rS  r‹   )rD   rL  rì  r  rj  rk  s   &&    r5   r   Úpearson3_gen._stats!  s(   € ØˆØˆØˆØ��a•�KˆØ�QˆzÐr7   c                óä   € \         P                  ! V P                  W4      4      pVP                  ^ 8X  d!   \         P                  ! V4      '       d   R# V# RV\         P                  ! V4      &   V# )r   r•   )rQ   rÓ   rý   rƒ  r-  )rD   rt   rL  rñ  s   &&& r5   ru   Úpearson3_gen._pdf !  sR   € ô
 �fŠf�T—\‘\ !Ó*Ó+ˆØ�8‰8�qŒ=Ü�xŠx˜�}Š}ÙØˆJØ ˆŒB�HŠH�S‹MÑØˆ
r7   c                óö   € V P                  W4      w  r1rErgr‰\        P                  ! \        W,          4      4      W5&   \        P                  ! \	        V4      4      \
        P                  WH4      ,           W6&   V# rO   )rô  rQ   r  rÖ   r	  r(  r5  )
rD   rt   rL  rñ  ró  r¼  rò  r©  rK  r  s
   &&&       r5   rý   Úpearson3_gen._logpdf-!  sa   € ð ×Ñ˜QÓ%ñ 	6ˆ�˜g¨Uô —F’Fœ9 Q¥WÓ-Ó.ˆ‰	ô —v’vœc $›iÓ(¬5¯<©<¸Ó+FÕFˆ‰Øˆ
r7   c                ó¸  € V P                  W4      w  r1rErgr‡\        W,          4      W5&   \        P                  ! W&P                  4      p\        P
                  ! Wb^ 8„  4      p	W&,          ^ 8„  p
\        P                  WJ,          WŠ,          4      W9&   \        P
                  ! Wb^ 8  4      pW&,          ^ 8  p\        P                  WL,          WŒ,          4      W;&   V# r  )	rô  rÜ   rQ   rv  rG  r  r(  r¯   r£  ©rD   rt   rL  rñ  ró  r¼  rò  r  rK  Ú	invmask1aÚ	invmask1bÚ	invmask2aÚ	invmask2bs   &&&          r5   ry   Úpearson3_gen._cdf<!  s´   € à×Ñ˜QÓ%ñ 	3ˆ�˜g¨%ô ˜a�gÓ&ˆ‰	ä�Š˜t§]¡]Ó3ˆÜ—N’N 7°1©HÓ5ˆ	Ø•M AÑ%ˆ	ô Ÿ™ 6Õ#4°eÕ6FÓGˆ‰ô —N’N 7°1©HÓ5ˆ	Ø•M AÑ%ˆ	äŸ™ &Õ"3°UÕ5EÓFˆ‰àˆ
r7   c                ó¸  € V P                  W4      w  r1rErgr‡\        W,          4      W5&   \        P                  ! W&P                  4      p\        P
                  ! Wb^ 8„  4      p	W&,          ^ 8„  p
\        P                  WJ,          WŠ,          4      W9&   \        P
                  ! Wb^ 8  4      pW&,          ^ 8  p\        P                  WL,          WŒ,          4      W;&   V# r  )	rô  ræ   rQ   rv  rG  r  r(  r£  r¯   r  s   &&&          r5   r~   Úpearson3_gen._sfT!  s°   € à×Ñ˜QÓ%ñ 	3ˆ�˜g¨%ô ˜Q�WÓ%ˆ‰	ä�Š˜t§]¡]Ó3ˆÜ—N’N 7°1©HÓ5ˆ	Ø•M AÑ%ˆ	ÜŸ™ &Õ"3°UÕ5EÓFˆ‰ä—N’N 7°1©HÓ5ˆ	Ø•M AÑ%ˆ	ÜŸ™ 6Õ#4°eÕ6FÓGˆ‰àˆ
r7   c                ó2  € \         P                  ! W4      pV P                  ^ .V4      w  p rVrxršVP                  4       pVP                  V,
          pVP                  V4      WF&   VP                  Wœ4      V,          V
,           WG&   VR8X  d
   V^ ,          pV# )r   r‹   )rQ   rv  rô  rè  rô   rò   r…  )rD   rL  rô   rõ   rñ  r  r¼  rò  r©  rK  r¸  ÚnsmallÚnbigs   &&&&         r5   rö   Úpearson3_gen._rvse!  s�   € Ü�Š˜tÓ*ˆà×Ñ˜a˜S $Ó'ñ 	4ˆˆQ�˜¨ð —‘“ˆØ�y‰y˜6Õ!ˆØ ×0Ñ0°Ó8ˆ‰	Ø#×2Ñ2°5Ó?ÀÕDÀtÕKˆ‰à�2Œ:Ø�a•&ˆCØˆ
r7   c                óâ   € V P                  W4      w  r1rErgr‰\        W,          4      W5&   W,          p^W^ 8  ,          ,
          W^ 8  &   \        P                  ! W�4      V,          V	,           W6&   V# r_   )rô  rã   r|   rK  )
rD   rƒ   rL  rñ  r  r¼  rò  r©  rK  r¸  s
   &&&       r5   r„   Úpearson3_gen._ppfs!  sf   € à×Ñ˜QÓ%ñ 	4ˆ�˜¨ä˜a�gÓ&ˆ‰	Ø�JˆØ˜! 1™H�+•oˆ�‰(‰Ü—~’~ eÓ/°Õ4°tÕ;ˆ‰Øˆ
r7   ze        Note that method of moments (`method='MM'`) is not
        available for this distribution.

r  c                ó‚   <€ VP                  R R4      R8X  d   \        R4      h\        \        V 4      V `  ! V.VO5/ VB # )r0   NÚMMzhFit `method='MM'` is not available for the Pearson3 distribution. Please try the default `method='MLE'`.)r<   ÚNotImplementedErrorr@   rA   rB   rÀ  s   &&*,€r5   rB   Úpearson3_gen.fit|!  sO   ø€ ð
 �8‰8�H˜dÓ# tÔ+Ü%ð 'Dó Eð Eô œ˜d› TÒ.¨tÐC°dÒC¸dÑCÐCr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rô  rd   rm   r   ru   rý   ry   r~   rö   r„   rK   r	   r   rB   r‘   r’   r  r   s   @@r5   rî  rî  Å   so   ù‡ € ñ,òZ@ò8!òNòòòòò0ô"òð Ù˜}ð 50ô 1ôDó1ó ÷Dð Dr7   rî  Úpearson3c                   ó¢   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 tR tR tV 3R lt]]! ]RR7      V 3R l4       4       tRtVtV ;t# )Úpowerlaw_geniŒ!  a  A power-function continuous random variable.

%(before_notes)s

See Also
--------
pareto

Notes
-----
The probability density function for `powerlaw` is:

.. math::

    f(x, a) = a x^{a-1}

for :math:`0 \le x \le 1`, :math:`a > 0`.

`powerlaw` takes ``a`` as a shape parameter for :math:`a`.

%(after_notes)s

For example, the support of `powerlaw` can be adjusted from the default
interval ``[0, 1]`` to the interval ``[c, c+d]`` by setting ``loc=c`` and
``scale=d``. For a power-law distribution with infinite support, see
`pareto`. For a power-law distribution described by PDF:

.. math::

    f(x; a, l, h) = \frac{a}{h^a - l^2} x^{a-1}

with :math:`a \neq 0` and :math:`0 < l < x < h`, see `truncpareto`.

`powerlaw` is a special case of `beta` with ``b=1``.

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r3  rj   rl   s   &r5   rm   Úpowerlaw_gen._shape_info³!  r6  r7   c                ó.   € W!VR ,
          ,          ,          # r8  r‹   r9  s   &&&r5   ru   Úpowerlaw_gen._pdf¶!  s   € à�Q�s•U•�|Ðr7   c                ót   € \         P                  ! V4      \        P                  ! V^,
          V4      ,           # r_   )rQ   r  r|   rµ  r9  s   &&&r5   rý   Úpowerlaw_gen._logpdfº!  s$   € Ü�vŠv�a‹yœ2Ÿ8š8 A¨¥E¨1Ó-Õ-Ð-r7   c                ó    € WR ,          ,          # r8  r‹   r9  s   &&&r5   ry   Úpowerlaw_gen._cdf½!  s   € Ø�S•5�zÐr7   c                ó<   € V\         P                  ! V4      ,          # rO   rc  r9  s   &&&r5   r  Úpowerlaw_gen._logcdfÀ!  re  r7   c                ó(   € \        VR V,          4      # r8  r:  rA  s   &&&r5   r„   Úpowerlaw_gen._ppfÃ!  s   € Ü�1�c˜!•e‹}Ðr7   c                ó0   € \         P                  ! W4      ) # rO   )r|   r­  )rD   rH  r˜   s   &&&r5   r~   Úpowerlaw_gen._sfÆ!  s   € Ü—’˜“ˆÐr7   c                ó    € W"V,           ,          # rO   r‹   r˜  s   &&&r5   r,  Úpowerlaw_gen._munpÉ!  s   € à˜•E�{Ðr7   c                óv  € WR ,           ,          WR,           ,          VR ,           ^,          ,          RVR ,
          VR,           ,          ,          \         P                  ! VR,           V,          4      ,          ^\         P                  ! . ROV4      ,          WR,           ,          V^,           ,          ,          3# )r–   rÒ   r£  rö  )rM   r  rà  rÑ   )rQ   r'  rØ
  rG  s   &&r5   r   Úpowerlaw_gen._statsÍ!  s   € Ø˜•W•Ø˜•W•  S¥¨Q¥Õ.Ø˜˜S� Q¨¥WÕ-Õ.´·²¸!¸c½'ÀQ½Ó1GÕGØ”B—J’Jš~¨qÓ1Õ1°Q¸c½'µ]ÀaÈ!ÅeÕ5LÕMðOð 	Or7   c                óX   € ^RV,          ,
          \         P                  ! V4      ,
          # r&  rc  rG  s   &&r5   r  Úpowerlaw_gen._entropyÓ!  rÂ  r7   c                óJ   <€ \         SV `  W4      V^ 8g  V^8¬  ,          ,          # r  )r@   rJ  )rD   rt   r˜   rØ  s   &&&€r5   rJ  Úpowerlaw_gen._support_maskÖ!  s*   ø€ Ü‘Ñ% aÓ+Ø˜‘F˜q A™vÕ&õ(ð 	)r7   a:          Notes specifically for ``powerlaw.fit``: If the location is a free
        parameter and the value returned for the shape parameter is less than
        one, the true maximum likelihood approaches infinity. This causes
        numerical difficulties, and the resulting estimates are approximate.
        

r  c                óô  <aaaaaaaa€ VP                  R R4      '       d   \        SV `  ! S.VO5/ VB # \        \        P
                  ! S4      4      ^8X  d   \        SV `  ! S.VO5/ VB # \        V SW#4      w  oorESV P                  S4      3.pV P                  V/ 4      ^,          pVeO   SP                  4       V8”  g   \        R^ ^4      hVe)   SP                  4       WE,           8:  g   \        R^ ^4      hVe;   V^ 8:  d   \        R4      hV\        P                  ! S4      8:  d   Rp\        V4      hR oR oVe   Ve   S! SWE4      WE3# Ve¹   \        P                  ! SP                  4       \        P                  ) 4      p	S;'       g
    S! SW•4      p
V! W©V3S4      p\        P                  ! SP                  4       V,
          \        P                  4      pS;'       g
    S! SWÅ4      pV! WÜV3S4      pW¾8  d   W©V3# WÜV3# Ve!   S! SV4      pS;'       g
    S! SWO4      pVWO3# VVVV3R lpR oR	 oVVVVV3R
 loVVVVVV3R loVVVVVV3R lpSe   S^8:  d   V! 4       # Se   S^8”  d   V! 4       # V! 4       pV P!                  VS4      pV! 4       pV P!                  VS4      pW¾8:  d   V^ ,          ^8:  d   V# W¾8”  d   V^ ,          ^8”  d   V# \        SV `  ! S.VO5/ VB # )rE  FÚpowerlawzKNegative or zero `fscale` is outside the range allowed by the distribution.z0`fscale` must be greater than the range of data.c                 óÌ   € \        V 4      pV) \        P                  ! \        P                  ! W,
          4      4      V\        P                  ! V4      ,          ,
          ,          # rO   )rç  rQ   rè  r  )rE   r-   r.   rñ  s   &&& r5   rÈ  Ú#powerlaw_gen.fit.<locals>.get_shape"  s?   € ô �D“	ˆAØ�3œ"Ÿ&š&¤§¢¨­
Ó!3Ó4°q¼¿ºÀ»µÕFÕGÐGr7   c                 ó0   € V P                  4       V,
          # rO   )r.  )rE   r-   s   &&r5   Ú	get_scaleÚ#powerlaw_gen.fit.<locals>.get_scale%"  s   € ð —8‘8“: Õ#Ð#r7   c                  ó  <€ \         P                  ! SP                  4       \         P                  ) 4      p \         P                  ! V 4      \         P
                  ! V P                  4      P                  8  dF   \         P                  ! V 4      \         P
                  ! V P                  4      P                  ,          p \         P                  ! S! SV 4      \         P                  4      pS;'       g
    S! SW4      pW V3# rO   )	rQ   rí
  rR  rk   r	  rÞ  r	  rß  rR   )r-   r.   rG  rE   rß
  r1  rÈ  s      €€€€r5   Úfit_loc_scale_w_shape_lt_1Ú4powerlaw_gen.fit.<locals>.fit_loc_scale_w_shape_lt_1L"  s¡   ø€ Ü—,’,˜tŸx™x›z¬B¯F©F¨7Ó3ˆCÜ�vŠv�c‹{œRŸXšX c§i¡iÓ0×5Ñ5Ô5Ü—g’g˜c“l¤R§X¢X¨c¯i©iÓ%8×%=Ñ%=Õ=�Ü—L’L¡¨4°Ó!5´r·v±vÓ>ˆEØ×9Ð9™i¨¨cÓ9ˆEØ˜uÐ$Ð$r7   c                 óF   € V P                   ^ ,          ) V,          V,          # r  )rG  )rE   rG  r.   s   &&&r5   rË  Ú#powerlaw_gen.fit.<locals>.dL_dScale["  s   € ð —J‘J˜q•M�> EÕ)¨EÕ1Ð1r7   c                 ód   € V^,
          \         P                  ! ^W ,
          ,          4      ,          # r_   r×  )rE   rG  r-   s   &&&r5   rÎ  Ú&powerlaw_gen.fit.<locals>.dL_dLocation`"  s#   € ð ˜A•I¤§¢¨¨S­ZÕ(8Ó!9Õ9Ð9r7   c                 ó–   <€ \         P                  ! S! SV 4      \         P                  ) 4      pS;'       g
    S! SW4      pS! SW 4      # rO   ©rQ   rí
  rk   )r-   r.   rG  rÎ  rE   rß
  r1  rÈ  s   &  €€€€€r5   ÚdL_dLocation_starÚ+powerlaw_gen.fit.<locals>.dL_dLocation_stare"  sC   ø€ ô —L’L¡¨4°Ó!5¼¿¹°wÓ?ˆEØ×9Ð9™i¨¨cÓ9ˆEÙ  eÓ1Ð1r7   c                 ó²   <€ \         P                  ! S! SV 4      \         P                  ) 4      pS;'       g
    S! SW4      pS! SW!4      S! SW 4      ,
          # rO   r;  )	r-   r.   rG  rÎ  rË  rE   rß
  r1  rÈ  s	   &  €€€€€€r5   rÚ  Ú&powerlaw_gen.fit.<locals>.fun_to_solvel"  sT   ø€ ô —L’L¡¨4°Ó!5¼¿¹°wÓ?ˆEØ×9Ð9™i¨¨cÓ9ˆEÙ˜d EÓ1Ù" 4¨Ó4õ5ð 6r7   c                  ó¾  <€ \         P                  ! S
P                  4       \         P                  ) 4      p S
P                  4       V ,
          pS	! V 4      ^ 8”  d#   S
P                  4       V,
          p V^,          pK/  V3R lpV ^,
          pRpV! W04      '       g9   V\         P                  ) 8w  d#   S
P                  4       V,
          pV^,          pKF  \        P
                  ! SW03R7      p\         P                  ! VP                  \         P                  ) 4      p\         P                  ! S! S
V4      \         P                  4      pS;'       g
    S! S
Wg4      pW†V3# )r   c                 óv   <€ \         P                  ! S! V 4      4      \         P                  ! S! V4      4      8g  # rO   rP   rÓ  s   &&€r5   rU   ÚTpowerlaw_gen.fit.<locals>.fit_loc_scale_w_shape_gt_1.<locals>.interval_contains_root€"  s/   ø€ äŸš¡¨VÓ 4Ó5ÜŸ7š7¡<°Ó#7Ó8ñ9ð :r7   r–   rÜ  )rQ   rí
  rR  rk   r   r*   rS  )rT   r6	  rU   rS   rS  rS  r-   r.   rG  r<  rE   rß
  rÚ  r1  rÈ  s            €€€€€€r5   Úfit_loc_scale_w_shape_gt_1Ú4powerlaw_gen.fit.<locals>.fit_loc_scale_w_shape_gt_1t"  s
  ø€ ô —\’\ $§(¡(£*¬r¯v©v¨gÓ6ˆFð —X‘X“Z &Õ(ˆEÙ# FÓ+¨aÔ/ØŸ™› eÕ+�Ø˜•
’õ:ð
 ˜a•ZˆFð
 ˆAÙ-¨f×=Ò=Ø¤"§&¡& Ô(ØŸ(™(›* q�.�Ø�Q•’ä×'Ò'¨¸vÐ>NÔOˆDä—,’,˜tŸy™y¬2¯6©6¨'Ó2ˆCÜ—L’L¡¨4°Ó!5´r·v±vÓ>ˆEØ×9Ð9™i¨¨cÓ9ˆEØ˜uÐ$Ð$r7   )r2   r@   rB   rç  rQ   ÚuniquerR  r×  Ú_reduce_funcrR  rƒ  r.  r"  Úptprí
  rk   rè
  )rD   rE   rF   r4   r  r  Úpenalized_nllf_argsÚpenalized_nllfrZ   Úloc_lt1Ú	shape_lt1Úll_lt1Úloc_gt1Ú	shape_gt1Úll_gt1r.   rG  r4  rC  Úfit_shape_lt1Úfit_shape_gt1rÎ  r<  rË  rß
  rÚ  r1  rÈ  rØ  s   &f*,                 @@@@@@@€r5   rB   Úpowerlaw_gen.fitÚ!  s  ÿø€ ðP �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3äŒr�yŠy˜‹Ó 1Ô$Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä%@ÀÀtØAEó&MÑ"ˆˆf�dà# d§n¡n°TÓ&:Ð%<Ð=ÐØ×*Ñ*Ð+>ÀÓCÀAÕFˆð
 ÒØ—8‘8“: Ô$Ü" :¨q°!Ó4Ð4ØÒ!¨$¯(©(«*¸½Ô*EÜ" :¨q°!Ó4Ð4àÒØ˜Œ{Ü ð "Fó Gð GàœŸš ›Ô%ØH�Ü  “oÐ%ò	Hò	$ð Ò $Ò"2Ù˜T 4Ó0°$Ð>Ð>ð Òä—l’l 4§8¡8£:´·±¨wÓ7ˆGØ×BÐB¡)¨D°'Ó"BˆIÙ# Y¸Ð$@À$ÓGˆFô —l’l 4§8¡8£:°Õ#6¼¿¹Ó?ˆGØ×BÐB¡)¨D°'Ó"BˆIÙ# Y¸Ð$@À$ÓGˆFàŒØ ¨6Ð1Ð1à ¨6Ð1Ð1ð ÒÙ˜d DÓ)ˆEØ×:Ð:™i¨¨dÓ:ˆEØ˜$Ð%Ð%÷
	%ð 	%ò	2ò
	:÷
	2ñ 	2÷	6ò 	6÷!	%ò !	%ðH Ò &¨A¤+Ù-Ó/Ð/ØÒ F¨Q¤JÙ-Ó/Ð/ñ 3Ó4ˆØ—‘˜=¨$Ó/ˆá2Ó4ˆØ—‘˜=¨$Ó/ˆàÔ ¨aÕ 0°AÔ 5Ø Ð ØŒ_ ¨qÕ!1°AÔ!5Ø Ð ä‘7’;˜tÐ3 dÒ3¨dÑ3Ð3r7   r‹   )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r  r„   r~   r,  r   r  rJ  rK   r	   r   rB   r‘   r’   r  r   s   @@r5   r  r  Œ!  st   ù‡ € ñ%òLEòò.òòòòòòOò%õ)ð Ù˜}ð 5ô ôH4óó ÷H4ð H4r7   r  r-  c                   ól   a € ] tR tRt o Rt]P                  tR tR t	R t
R tR tR tR	 tR
 tRtV tR# )Úpowerlognorm_geni¯"  a½  A power log-normal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `powerlognorm` is:

.. math::

    f(x, c, s) = \frac{c}{x s} \phi(\log(x)/s)
                 (\Phi(-\log(x)/s))^{c-1}

where :math:`\phi` is the normal pdf, and :math:`\Phi` is the normal cdf,
and :math:`x > 0`, :math:`s, c > 0`.

`powerlognorm` takes :math:`c` and :math:`s` as shape parameters.

%(after_notes)s

%(example)s

c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# )r\  Frj  r4  rj   )rD   ry  r-  s   &  r5   rm   Úpowerlognorm_gen._shape_infoÉ"  r/  r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  ©rD   rt   r\  rj  s   &&&&r5   ru   Úpowerlognorm_gen._pdfÎ"  rÌ  r7   c                ód  € \         P                  ! V4      \         P                  ! V4      ,
          \         P                  ! V4      ,
          \        \         P                  ! V4      V,          4      ,           \        \         P                  ! V4      ) V,          4      VR ,
          ,          ,           # r8  ©rQ   r  rÙ   rß   rX  s   &&&&r5   rý   Úpowerlognorm_gen._logpdfÑ"  si   € Ü—’�q“	œBŸFšF 1›IÕ%¬¯ª¨q«	Õ1ÜœRŸVšV A›Y¨�]Ó+õ,äœbŸfšf Q›i˜Z¨!�^Ó,°°BµÕ7õ8ð 	9r7   c                óP   € \         P                  ! V P                  WV4      4      ) # rO   rÈ  rX  s   &&&&r5   ry   Úpowerlognorm_gen._cdfÖ"  rÊ  r7   c                ó4   € V P                  ^V,
          W#4      # r_   )rˆ   ©rD   rƒ   r\  rj  s   &&&&r5   r„   Úpowerlognorm_gen._ppfÙ"  s   € Ø�y‰y˜˜Q� Ó%Ð%r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r“  rX  s   &&&&r5   r~   Úpowerlognorm_gen._sfÜ"  r•  r7   c                ó^   € \        \        P                  ! V4      ) V,          4      V,          # rO   rb  rX  s   &&&&r5   r
  Úpowerlognorm_gen._logsfß"  s    € ÜœRŸVšV A›Y˜J¨�NÓ+¨aÕ/Ð/r7   c                ól   € \         P                  ! \        V^V,          ,          4      ) V,          4      # r_   rÊ
  r`  s   &&&&r5   rˆ   Úpowerlognorm_gen._isfâ"  s&   € Ü�vŠv”y  Q q¥S¥Ó*Ð*¨QÕ.Ó/Ð/r7   r‹   N)rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   ru   rý   ry   r„   r~   r
  rˆ   r‘   r’   r“   s   @r5   rT  rT  ¯"  sD   ø‡ € ñð. "×4Ñ4€Mòò
-ò9ò
/ò&ò,ò0÷0ð 0r7   rT  Úpowerlognormc                   óT   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tRtV tR# )Úpowernorm_genié"  a(  A power normal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `powernorm` is:

.. math::

    f(x, c) = c \phi(x) (\Phi(-x))^{c-1}

where :math:`\phi` is the normal pdf, :math:`\Phi` is the normal cdf,
:math:`x` is any real, and :math:`c > 0` [1]_.

`powernorm` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

References
----------
.. [1] NIST Engineering Statistics Handbook, Section 1.3.6.6.13,
       https://www.itl.nist.gov/div898/handbook//eda/section3/eda366d.htm

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úpowernorm_gen._shape_info#  r6  r7   c                ód   € V\        V4      ,          \        V) 4      VR ,
          ,          ,          # r8  ©rÖ   rÜ   r`  s   &&&r5   ru   Úpowernorm_gen._pdf#  s$   € à”˜1“�~¤¨A¨2£°°3µÕ!7Õ8Ð8r7   c                óŒ   € \         P                  ! V4      \        V4      ,           V^,
          \        V) 4      ,          ,           # r_   r[  r`  s   &&&r5   rý   Úpowernorm_gen._logpdf#  s.   € Ü�vŠv�a‹yœ<¨›?Õ*¨a°­c´<ÀÀÓ3CÕ-CÕCÐCr7   c                óN   € \         P                  ! V P                  W4      4      ) # rO   rÈ  r`  s   &&&r5   ry   Úpowernorm_gen._cdf#  s   € Ü—’˜Ÿ™ QÓ*Ó+Ð+Ð+r7   c                óJ   € \        \        R V,
          R V,          4      4      ) # r8  )rã   r¨  rg  s   &&&r5   r„   Úpowernorm_gen._ppf#  s   € Üœ#˜c A�g s¨Q¥wÓ/Ó0Ð0Ð0r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r“  r`  s   &&&r5   r~   Úpowernorm_gen._sf#  r8  r7   c                ó(   € V\        V) 4      ,          # rO   rè   r`  s   &&&r5   r
  Úpowernorm_gen._logsf#  s   € Ø”<  Ó#Õ#Ð#r7   c                óx   € \        \        P                  ! \        P                  ! V4      V,          4      4      ) # rO   )rã   rQ   rÓ   r  rg  s   &&&r5   rˆ   Úpowernorm_gen._isf#  s%   € Üœ"Ÿ&š&¤§¢¨£¨Q¥Ó/Ó0Ð0Ð0r7   r‹   N)rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   r
  rˆ   r‘   r’   r“   s   @r5   rj  rj  é"  s9   ø‡ € ñò6Eò9òDò,ò1ò)ò$÷1ð 1r7   rj  Ú	powernormc                   óX   a € ] tR tRt o RtR tR tR tR tR t	R t
RR
 ltR tRtV tR	# )Ú	rdist_geni"#  aÛ  An R-distributed (symmetric beta) continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `rdist` is:

.. math::

    f(x, c) = \frac{(1-x^2)^{c/2-1}}{B(1/2, c/2)}

for :math:`-1 \le x \le 1`, :math:`c > 0`. `rdist` is also called the
symmetric beta distribution: if B has a `beta` distribution with
parameters (c/2, c/2), then X = 2*B - 1 follows a R-distribution with
parameter c.

`rdist` takes ``c`` as a shape parameter for :math:`c`.

This distribution includes the following distribution kernels as
special cases::

    c = 2:  uniform
    c = 3:  `semicircular`
    c = 4:  Epanechnikov (parabolic)
    c = 6:  quartic (biweight)
    c = 8:  triweight

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r[  rj   rl   s   &r5   rm   Úrdist_gen._shape_infoD#  r6  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  r`  s   &&&r5   ru   Úrdist_gen._pdfH#  r`  r7   c                ó    € \         P                  ! ^4      ) \        P                  V^,           ^,          V^,          V^,          4      ,           # rD  )rQ   r  r©  rý   r`  s   &&&r5   rý   Úrdist_gen._logpdfK#  s4   € Ü—’�q“	ˆzœDŸL™L¨!¨a­%°­°A°aµC¸¸1½Ó=Õ=Ð=r7   c                óh   € \         P                  V^,           ^,          V^,          V^,          4      # r_   r<  r`  s   &&&r5   ry   Úrdist_gen._cdfN#  s%   € Ü�y‰y˜!˜a�% � A a¥C¨¨1­Ó-Ð-r7   c                óh   € \         P                  V^,           ^,          V^,          V^,          4      # r_   r5  r`  s   &&&r5   r~   Úrdist_gen._sfQ#  s%   € Ü�x‰x˜˜Q� �	 1 Q¥3¨¨!­Ó,Ð,r7   c                óf   € ^\         P                  W^,          V^,          4      ,          ^,
          # rD  )r©  r„   rg  s   &&&r5   r„   Úrdist_gen._ppfT#  s%   € Ø”—‘˜1 �c 1 Q¥3Ó'Õ'¨!Õ+Ð+r7   Nc                ó`   € ^VP                  V^,          V^,          V4      ,          ^,
          # rD  r¨  rÖ  s   &&&&r5   rö   Úrdist_gen._rvsW#  s)   € Ø�<×$Ñ$ Q q¥S¨!¨A­#¨tÓ4Õ4°qÕ8Ð8r7   c                óÎ   € ^V^,          ,
          \         P                  ! VR,           ^,          VR,          4      ,          pV\         P                  ! RVR,          4      ,          # )rM   r–   rÒ   r£   r·  )rD   rc   r\  Ú	numerators   &&& r5   r,  Úrdist_gen._munpZ#  sE   € Ø˜!˜a�%•[¤B§G¢G¨Q°­W¸­M¸1¸s½7Ó$CÕCˆ	Øœ2Ÿ7š7 6¨1¨r­6Ó2Õ2Ð2r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r~   r„   rö   r,  r‘   r’   r“   s   @r5   r~  r~  "#  s9   ø‡ € ñ òBEò*ò>ò.ò-ò,ô9÷3ð 3r7   r~  Úrdistc                   ó¸   a a€ ] tR tRt oRt]P                  tR tRR lt	R t
R tR tR tR	 tR
 tR tR tR t]]! ]RR7      V 3R l4       4       tRtVtV ;t# )Úrayleigh_genib#  a  A Rayleigh continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `rayleigh` is:

.. math::

    f(x) = x \exp(-x^2/2)

for :math:`x \ge 0`.

`rayleigh` is a special case of `chi` with ``df=2``.

%(after_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úrayleigh_gen._shape_infoz#  r¼   r7   c                ó0   € \         P                  ^WR7      # )rÑ   r'  r  ró   s   &&&r5   rö   Úrayleigh_gen._rvs}#  s   € Ü�w‰w�q˜tˆwÓ?Ð?r7   c                óL   € \         P                  ! V P                  V4      4      # rO   r.  ©rD   rI  s   &&r5   ru   Úrayleigh_gen._pdf€#  ry  r7   c                óX   € \         P                  ! V4      R V,          V,          ,
          # r  rc  r˜  s   &&r5   rý   Úrayleigh_gen._logpdf„#  s   € Ü�vŠv�a‹y˜3 �7 Q�;Õ&Ð&r7   c                óL   € \         P                  ! RV^,          ,          4      ) # r¹  r=  r˜  s   &&r5   ry   Úrayleigh_gen._cdf‡#  s   € Ü—’˜  1¥�Ó%Ð%Ð%r7   c                óf   € \         P                  ! R\        P                  ! V) 4      ,          4      # ©rÑ   r<  )rQ   r'  r|   ré  rÉ   s   &&r5   r„   Úrayleigh_gen._ppfŠ#  s    € Ü�wŠw�rœBŸHšH a R›LÕ(Ó)Ð)r7   c                óL   € \         P                  ! V P                  V4      4      # rO   r“  r˜  s   &&r5   r~   Úrayleigh_gen._sf�#  s   € Ü�vŠv�d—k‘k !“nÓ%Ð%r7   c                ó"   € RV,          V,          # r¹  r‹   r˜  s   &&r5   r
  Úrayleigh_gen._logsf�#  s   € Ø�a�x˜!�|Ðr7   c                ód   € \         P                  ! R\         P                  ! V4      ,          4      # rŸ  )rQ   r'  r  rÉ   s   &&r5   rˆ   Úrayleigh_gen._isf“#  s   € Ü�wŠw�rœBŸFšF 1›I•~Ó&Ð&r7   c                ó¤  € ^\         P                  ,
          p\         P                  ! \         P                  ^,          4      V^,          ^\         P                  ^,
          ,          \         P                  ! \         P                  4      ,          VR,          ,          ^\         P                  ,          V,          ^V^,          ,          ,
          3# ©rU  rS  r#  r$  s   & r5   r   Úrayleigh_gen._stats–#  sy   € Ø”"—%‘%�iˆÜ—’œŸ™˜a�Ó Ø�A•Ø”2—5‘5˜•7•œBŸGšG¤B§E¡E›NÕ*¨3°­8Õ3Ø”"—%‘%•˜•˜B˜s A�v�IÕ%ð'ð 	'r7   c                ón   € \         R ,          ^,           R\        P                  ! ^4      ,          ,
          # )rÒ   r£   rA  rl   s   &r5   r  Úrayleigh_gen._entropy�#  s!   € Ü�c�z˜A�~ ¤B§F¢F¨1£I¥Õ-Ð-r7   aú          Notes specifically for ``rayleigh.fit``: If the location is fixed with
        the `floc` parameter, this method uses an analytical formula to find
        the scale.  Otherwise, this function uses a numerical root finder on
        the first order conditions of the log-likelihood function to find the
        MLE.  Only the (optional) `loc` parameter is used as the initial guess
        for the root finder; the `scale` parameter and any other parameters
        for the optimizer are ignored.

r  c                óü  <a€ VP                  R R4      '       d   \        SV `  ! S.VO5/ VB # \        V SW#4      w  orEV3R lpV3R lpV3V3R llpVeL   \        P
                  ! SV,
          ^ 8*  4      '       d   \        R^\        P                  R7      hWF! V4      3# VP                  R4      p	V	f   V P                  S4      ^ ,          p	Vf   TMTp
\        P                  ! \        P                  ! S4      \        P                  ) 4      p\        W«4      p\        P                  ! W¬V3R7      pVP                  '       g   \!        VP"                  4      hVP$                  pT;'       g	    V! V4      pWï3# )	rE  Fc                 óˆ   <€ \         P                  ! SV ,
          ^,          4      ^\        S4      ,          ,          R,          # rI  )rQ   rè  rç  )r-   rE   s   &€r5   Ú	scale_mleÚ#rayleigh_gen.fit.<locals>.scale_mle¯#  s/   ø€ ô —F’F˜D 3�J¨1Õ,Ó-°´S¸³YµÕ?ÀBÕFÐFr7   c                 óÞ   <€ SV ,
          pVP                  4       pV^,          P                  4       p^V,          P                  4       pW#^\        S4      ,          ,          V,          ,
          # rD  )rè  rç  )r-   r4	  r–  rœ  Ús3rE   s   &    €r5   Úloc_mleÚ!rayleigh_gen.fit.<locals>.loc_mle´#  sR   ø€ ð ˜•ˆBØ—‘“ˆBØ�a•%—‘“ˆBØ�B•$—‘“ˆBØ˜Aœc $›i�KÕ(¨Õ+Õ+Ð+r7   c                 óŠ   <€ SV ,
          pVP                  4       V^,          ^V,          P                  4       ,          ,
          # rD  )rè  )r-   r.   r4	  rE   s   && €r5   Úloc_mle_scale_fixedÚ-rayleigh_gen.fit.<locals>.loc_mle_scale_fixed½#  s2   ø€ ð ˜•ˆBØ—6‘6“8˜e Q�h¨!¨B­$¯©«Õ5Õ5Ð5r7   ÚrayleighrÛ  r-   rÜ  )r2   r@   rB   rR  rQ   ræ  rƒ  rk   r<   r×  rí
  rR  r[   r   r*   rî
  rX   ÚflagrS  )rD   rE   rF   r4   r  r  r®  r²  rµ  Úloc0rH   rT   rS   r›  r-   r.   rØ  s   &f*,            €r5   rB   Úrayleigh_gen.fit #  sG  ù€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3Ü8¸¸tØ9=óEÑˆˆdõ	Gõ
	,ð ,2÷ 	6ð Òä�vŠv�d˜T•k QÑ&×'Ò'Ü" :°Q¼b¿f¹fÔEÐEà˜Y t›_Ð,Ð,ð �x‰x˜‹ˆØŠ<à—>‘> $Ó'¨Õ*ˆDàš‰gÐ-@ˆÜ—’œbŸfšf T›l¬R¯V©V¨GÓ4ˆÜ" 3Ó/ˆÜ×"Ò" 3¸Ð0@ÔAˆØ�}�}ˆ}Ü  §¡Ó*Ð*Ø�h‰hˆØ×(Ð(™) C›.ˆØˆzÐr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   rö   ru   rý   ry   r„   r~   r
  rˆ   r   r  rK   r	   rB   r‘   r’   r  r   s   @@r5   r’  r’  b#  s|   ù‡ € ñð* "×4Ñ4€Mòô@ò'ò'ò&ò*ò&òò'ò'ò.ð Ù˜}ð 5.ô /ô/ó/ó ÷/ð /r7   r’  r·  c                   ó–   a a€ ] tR tRt oRtR tR tV 3R ltR tR t	R t
R	 tR
 tR tR tRt]! ]]R7      V 3R l4       tRtVtV ;t# )Úreciprocal_geniÞ#  aœ  A loguniform or reciprocal continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for this class is:

.. math::

    f(x, a, b) = \frac{1}{x \log(b/a)}

for :math:`a \le x \le b`, :math:`b > a > 0`. This class takes
:math:`a` and :math:`b` as shape parameters.

%(after_notes)s

%(example)s

This doesn't show the equal probability of ``0.01``, ``0.1`` and
``1``. This is best when the x-axis is log-scaled:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
>>> ax.hist(np.log10(r))
>>> ax.set_ylabel("Frequency")
>>> ax.set_xlabel("Value of random variable")
>>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
>>> ticks = ["$10^{{ {} }}$".format(i) for i in [-2, -1, 0]]
>>> ax.set_xticklabels(ticks)  # doctest: +SKIP
>>> plt.show()

This random variable will be log-uniform regardless of the base chosen for
``a`` and ``b``. Let's specify with base ``2`` instead:

>>> rvs = %(name)s(2**-2, 2**0).rvs(size=1000)

Values of ``1/4``, ``1/2`` and ``1`` are equally likely with this random
variable.  Here's the histogram:

>>> fig, ax = plt.subplots(1, 1)
>>> ax.hist(np.log2(rvs))
>>> ax.set_ylabel("Frequency")
>>> ax.set_xlabel("Value of random variable")
>>> ax.xaxis.set_major_locator(plt.FixedLocator([-2, -1, 0]))
>>> ticks = ["$2^{{ {} }}$".format(i) for i in [-2, -1, 0]]
>>> ax.set_xticklabels(ticks)  # doctest: +SKIP
>>> plt.show()

c                ó   € V^ 8„  W!8„  ,          # r  r‹   r	  s   &&&r5   rd   Úreciprocal_gen._argcheck$  s   € Ø�A‘˜!™%Õ Ð r7   c                ó€   € \        R R^ \        P                  3R4      p\        RR^ \        P                  3R4      pW.# r¡  rj   r¢  s   &  r5   rm   Úreciprocal_gen._shape_info$  r¦  r7   c                óÆ   <€ \        V\        4      '       d   VP                  4       p\        SV `  V\
        P                  ! V4      \
        P                  ! V4      3R 7      # r)	  ©r>   r)   rÕ  r@   r×  rQ   rR  r.  rb  s   &&€r5   r×  Úreciprocal_gen._fitstart$  sF   ø€ Ü�dœL×)Ò)Ø—>‘>Ó#ˆDä‰wÑ  ¬R¯VªV°D«\¼2¿6º6À$»<Ð,HÐ ÓIÐIr7   c                ó   € W3# rO   r‹   r	  s   &&&r5   r¥   Úreciprocal_gen._get_support $  rf  r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  r°  s   &&&&r5   ru   Úreciprocal_gen._pdf#$  r0  r7   c                óÄ   € \         P                  ! V4      ) \         P                  ! \         P                  ! V4      \         P                  ! V4      ,
          4      ,
          # rO   rc  r°  s   &&&&r5   rý   Úreciprocal_gen._logpdf'$  s5   € Ü—’�q“	ˆzœBŸFšF¤2§6¢6¨!£9¬r¯vªv°a«yÕ#8Ó9Õ9Ð9r7   c                óÐ   € \         P                  ! V4      \         P                  ! V4      ,
          \         P                  ! V4      \         P                  ! V4      ,
          ,          # rO   rc  r°  s   &&&&r5   ry   Úreciprocal_gen._cdf*$  s7   € Ü—’�q“	œ"Ÿ&š& ›)Õ#¬¯ª¨q«	´B·F²F¸1³IÕ(=Õ>Ð>r7   c                óÐ   € \         P                  ! \         P                  ! V4      V\         P                  ! V4      \         P                  ! V4      ,
          ,          ,           4      # rO   ©rQ   rÓ   r  rÄ  s   &&&&r5   r„   Úreciprocal_gen._ppf-$  s8   € Ü�vŠv”b—f’f˜Q“i !¤R§V¢V¨A£Y´·²¸³Õ%:Õ";Õ;Ó<Ð<r7   c                óv  € V^ 8X  d   R# ^\         P                  ! V4      \         P                  ! V4      ,
          ,          V,          p\         P                  ! \         P                  ! \	        V\         P                  ! V4      ,          V\         P                  ! V4      ,          4      4      4      pWE,          # r  )rQ   r  r  rÓ   Ú	_log_diff)rD   rc   r˜   r™   rû  rü  s   &&&&  r5   r,  Úreciprocal_gen._munp0$  sm   € Ø�Œ6ÙØ”"—&’&˜“)œbŸfšf Q›iÕ'Õ(¨1Õ,ˆÜ�WŠW”R—V’VœI a¬"¯&ª&°«)¥m°Q´r·v²v¸a³yµ[ÓAÓBÓCˆØ�wˆr7   c                ó  € R \         P                  ! V4      \         P                  ! V4      ,           ,          \         P                  ! \         P                  ! V4      \         P                  ! V4      ,
          4      ,           # r  rc  r	  s   &&&r5   r  Úreciprocal_gen._entropy7$  sE   € Ø”B—F’F˜1“I¤§¢ q£	Õ)Õ*¬R¯VªV´B·F²F¸1³IÄÇÂÀqÃ	Õ4IÓ-JÕJÐJr7   z“        `loguniform`/`reciprocal` is over-parameterized. `fit` automatically
         fixes `scale` to 1 unless `fscale` is provided by the user.

r  c                óT   <€ VP                  R ^4      p\        SV `  ! V.VO5R V/VB # )r  )r2   r@   rB   )rD   rE   rF   r4   r  rØ  s   &&*, €r5   rB   Úreciprocal_gen.fit>$  s1   ø€ à—‘˜( AÓ&ˆÜ‰wŠ{˜4Ð> $Ò>¨vÐ>¸Ñ>Ð>r7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   r×  r¥   ru   rý   ry   r„   r,  r  Úfit_noter	   r   rB   r‘   r’   r  r   s   @@r5   r¼  r¼  Þ#  sg   ù‡ € ñ2òf!òõ
Jòò-ò:ò?ò=òòKðL€Hñ ˜}°HÔ=ô?ó >÷?ð ?r7   r¼  Ú
loguniformÚ
reciprocalc                   óR   a € ] tR tRt o RtR tR tRR ltR tR t	R	 t
R
 tRtV tR# )Úrice_geniN$  aÄ  A Rice continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `rice` is:

.. math::

    f(x, b) = x \exp(- \frac{x^2 + b^2}{2}) I_0(x b)

for :math:`x >= 0`, :math:`b > 0`. :math:`I_0` is the modified Bessel
function of order zero (`scipy.special.i0`).

`rice` takes ``b`` as a shape parameter for :math:`b`.

%(after_notes)s

The Rice distribution describes the length, :math:`r`, of a 2-D vector with
components :math:`(U+u, V+v)`, where :math:`U, V` are constant, :math:`u,
v` are independent Gaussian random variables with standard deviation
:math:`s`.  Let :math:`R = \sqrt{U^2 + V^2}`. Then the pdf of :math:`r` is
``rice.pdf(x, R/s, scale=s)``.

%(example)s

c                ó   € V^ 8¬  # r  r‹   rÀ  s   &&r5   rd   Úrice_gen._argcheckk$  rÏ  r7   c                ó@   € \        R R^ \        P                  3R4      .# )r™   Fri   rj   rl   s   &r5   rm   Úrice_gen._shape_infon$  rÓ  r7   Nc                óÐ   € V\         P                  ! ^4      ,          VP                  RV,           R7      ,           p\         P                  ! WD,          P                  ^ R7      4      # )rÑ   r³  rO  rD  )rQ   r'  rò   rè  )rD   r™   rô   rõ   r±  s   &&&& r5   rö   Úrice_gen._rvsq$  sF   € àŒb�gŠg�a‹j�L˜<×7Ñ7¸TÀD½[Ð7ÓIÕIˆÜ�wŠw˜�—y‘y a�yÓ(Ó)Ð)r7   c                ó‚   € \         P                  ! \        P                  ! V4      ^\        P                  ! V4      4      # rD  )r|   r  rQ   rÝ  r—  s   &&&r5   ry   Úrice_gen._cdfv$  s%   € Ü�yŠyœŸš 1› q¬"¯)ª)°A«,Ó7Ð7r7   c           	     ó‚   € \         P                  ! \        P                  ! V^\         P                  ! V4      4      4      # rD  )rQ   r'  r|   r  rÝ  r©  s   &&&r5   r„   Úrice_gen._ppfy$  s&   € Ü�wŠw”r—{’{ 1 a¬¯ª°1«Ó6Ó7Ð7r7   c                ó´   € V\         P                  ! W,
          ) W,
          ,          R ,          4      ,          \        P                  ! W,          4      ,          # rr  )rQ   rÓ   r|   Úi0er—  s   &&&r5   ru   Úrice_gen._pdf|$  s6   € ð ”2—6’6˜A�C˜& !¥#�, sÕ*Ó+Õ+¬b¯fªf°QµS«kÕ9Ð9r7   c                óþ   € VR ,          p^V,           pW",          R ,          pR V,          \         P                  ! V) 4      ,          \        P                  ! V4      ,          \        P                  ! V^V4      ,          # rr  )rQ   rÓ   r|   r(  Úhyp1f1)rD   rc   r™   Únd2Ún1rJ  s   &&&   r5   r,  Úrice_gen._munp…$  s\   € Ø��eˆØ��WˆØ�S��WˆØ�c•
œRŸVšV R C›[Õ(¬2¯8ª8°B«<Õ7Ü—	’	˜"˜a Ó$õ%ð 	&r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rd   rm   rö   ry   r„   ru   r,  r‘   r’   r“   s   @r5   rÚ  rÚ  N$  s3   ø‡ € ñò8òDô*ò
8ò8ò:÷&ð &r7   rÚ  Úricec                   óŽ   a € ] tR tRt o Rt]! ]RR7      R 4       tR tR t	R t
R	 t]R
 4       tR tR tR tRR ltR tRtV tR# )Úirwinhall_geni�$  a¢	  An Irwin-Hall (Uniform Sum) continuous random variable.

An `Irwin-Hall <https://en.wikipedia.org/wiki/Irwin-Hall_distribution/>`_
continuous random variable is the sum of :math:`n` independent
standard uniform random variables [1]_ [2]_.

%(before_notes)s

Notes
-----
Applications include `Rao's Spacing Test
<https://jammalam.faculty.pstat.ucsb.edu/html/favorite/test.htm>`_,
a more powerful alternative to the Rayleigh test
when the data are not unimodal, and radar [3]_.

Conveniently, the pdf and cdf are the :math:`n`-fold convolution of
the ones for the standard uniform distribution, which is also the
definition of the cardinal B-splines of degree :math:`n-1`
having knots evenly spaced from :math:`1` to :math:`n` [4]_ [5]_.

The Bates distribution, which represents the *mean* of statistically
independent, uniformly distributed random variables, is simply the
Irwin-Hall distribution scaled by :math:`1/n`. For example, the frozen
distribution ``bates = irwinhall(10, scale=1/10)`` represents the
distribution of the mean of 10 uniformly distributed random variables.

%(after_notes)s

References
----------
.. [1] P. Hall, "The distribution of means for samples of size N drawn
        from a population in which the variate takes values between 0 and 1,
        all such values being equally probable",
        Biometrika, Volume 19, Issue 3-4, December 1927, Pages 240-244,
        :doi:`10.1093/biomet/19.3-4.240`.
.. [2] J. O. Irwin, "On the frequency distribution of the means of samples
        from a population having any law of frequency with finite moments,
        with special reference to Pearson's Type II,
        Biometrika, Volume 19, Issue 3-4, December 1927, Pages 225-239,
        :doi:`0.1093/biomet/19.3-4.225`.
.. [3] K. Buchanan, T. Adeyemi, C. Flores-Molina, S. Wheeland and D. Overturf,
        "Sidelobe behavior and bandwidth characteristics
        of distributed antenna arrays,"
        2018 United States National Committee of
        URSI National Radio Science Meeting (USNC-URSI NRSM),
        Boulder, CO, USA, 2018, pp. 1-2.
        https://www.usnc-ursi-archive.org/nrsm/2018/papers/B15-9.pdf.
.. [4] Amos Ron, "Lecture 1: Cardinal B-splines and convolution operators", p. 1
        https://pages.cs.wisc.edu/~deboor/887/lec1new.pdf.
.. [5] Trefethen, N. (2012, July). B-splines and convolution. Chebfun.
        Retrieved April 30, 2024, from http://www.chebfun.org/examples/approx/BSplineConv.html.

%(example)s
zÞ        Raises a ``NotImplementedError`` for the Irwin-Hall distribution because
        the generic `fit` implementation is unreliable and no custom implementation
        is available. Consider using `scipy.stats.fit`.

r  c                ó   € R p\        V4      h)z’The generic `fit` implementation is unreliable for this distribution, and no custom implementation is available. Consider using `scipy.stats.fit`.)r  )rD   rE   rF   r4   Ú	fit_notess   &&*, r5   rB   Úirwinhall_gen.fitÇ$  s   € ð
9ˆ	ô " )Ó,Ð,r7   c                ób   € V^ 8„  \        V4      ,          \        P                  ! V4      ,          # r  )r   rQ   Ú	isrealobjrb   s   &&r5   rd   Úirwinhall_gen._argcheckÑ$  s"   € Ø�A‘œ Q›Õ'¬"¯,ª,°q«/Õ9Ð9r7   c                ó
   € ^ V3# r  r‹   rb   s   &&r5   r¥   Úirwinhall_gen._get_supportÔ$  s   € Ø�!ˆtˆr7   c                ó@   € \        R R^\        P                  3R4      .# rh   rj   rl   s   &r5   rm   Úirwinhall_gen._shape_info×$  ro   r7   c                ób   € R  p\         P                  ! V\         P                  .R7      ! W4      # )c                 óÔ   € \         P                  ! V\         P                  R 7      p\        P                  ! W,           VRR7      \        P
                  ! W,           VRR7      ,          # )r	  T)Úexact)rQ   r#  Úint64r|   Ú	stirling2rõ  )r/  rc   s   &&r5   ÚvmunpÚ"irwinhall_gen._munp.<locals>.vmunpÝ$  sD   € Ü—
’
˜1¤B§H¡HÔ-ˆAÜ—L’L ¥¨!°4Ô8Ü—g’g˜a�g q°Ô5õ6ð 7r7   r  r  )rD   r/  rc   rÿ  s   &&& r5   r,  Úirwinhall_gen._munpÚ$  s%   € ò	7ô �|Š|˜E¬2¯:©:¨,Õ7¸ÓAÐAr7   c                óh   € \         P                  ! V ^,           4      p\        P                  ! V4      # r_   )rQ   r¯  r   Úbasis_element)rc   r±  s   & r5   Ú	_cardbsplÚirwinhall_gen._cardbsplå$  s$   € ä�IŠI�a˜•c‹NˆÜ×$Ò$ QÓ'Ð'r7   c                ój   a € V 3R  lp\         P                  ! V\         P                  .R7      ! W4      # )c                 ó2   <€ SP                  V4      ! V 4      # rO   )r  ©rt   rc   rD   s   &&€r5   ÚvpdfÚ irwinhall_gen._pdf.<locals>.vpdfë$  s   ø€ Ø—>‘> !Ô$ QÓ'Ð'r7   r  r  )rD   rt   rc   r	  s   f&& r5   ru   Úirwinhall_gen._pdfê$  s$   ø€ õ	(ä�|Š|˜D¬"¯*©*¨Õ6°qÓ<Ð<r7   c                ój   a € V 3R  lp\         P                  ! V\         P                  .R7      ! W4      # )c                 óN   <€ SP                  V4      P                  4       ! V 4      # rO   ©r  Úantiderivativer  s   &&€r5   ÚvcdfÚ irwinhall_gen._cdf.<locals>.vcdfð$  s    ø€ Ø—>‘> !Ó$×3Ñ3Ô5°aÓ8Ð8r7   r  r  )rD   rt   rc   r  s   f&& r5   ry   Úirwinhall_gen._cdfï$  s$   ø€ õ	9ä�|Š|˜D¬"¯*©*¨Õ6°qÓ<Ð<r7   c                ój   a € V 3R  lp\         P                  ! V\         P                  .R7      ! W4      # )c                 óZ   <€ SP                  V4      P                  4       ! W,
          4      # rO   r  r  s   &&€r5   ÚvsfÚirwinhall_gen._sf.<locals>.vsfõ$  s"   ø€ Ø—>‘> !Ó$×3Ñ3Ô5°aµcÓ:Ð:r7   r  r  )rD   rt   rc   r  s   f&& r5   r~   Úirwinhall_gen._sfô$  s$   ø€ õ	;ä�|Š|˜C¬¯©¨Õ5°aÓ;Ð;r7   Nc                ó2   € \         RR l4       pV! WVR7      # )Nc                 ó²   € \         P                  ! V 4      P                  \        4      p Vf   V 3MV .VO5pVP	                  VR7      P                  ^ R7      # )Nr³  rO  )rQ   r  r‰  r+  r´  rè  )rc   rô   rõ   Úusizes   &&& r5   Ú_rvs1Ú!irwinhall_gen._rvs.<locals>._rvs1ú$  sO   € ä—’˜“×"Ñ"¤3Ó'ˆAØ šL�Q‘D¨q¨j°4©jˆEØ×'Ñ'¨UÐ'Ó3×7Ñ7¸QÐ7Ó?Ð?r7   r'  r.  )r   )rD   rc   rô   rõ   rF   r  s   &&&&* r5   rö   Úirwinhall_gen._rvsù$  s%   € Ü	#ó	@ó 
$ð	@ñ �Q°Ô=Ð=r7   c                óF   € V^,          V^,          ^ R^V,          ,          3# )rÑ   rà  r‹   rb   s   &&r5   r   Úirwinhall_gen._stats%  s#   € ð ��s�A�b•D˜!˜R  1¥�XÐ%Ð%r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r
   r   rB   rd   r¥   rm   r,  rT  r  ru   ry   r~   rö   r   r‘   r’   r“   s   @r5   rï  rï  �$  su   ø‡ € ñ5ñn   ð 6?ô @ñ-ó	@ð-ò:òòCò	Bð ñ(ó ð(ò=ò
=ò
<ô
>÷&ð &r7   rï  Ú	irwinhallc                   óL   a € ] tR tRt o RtR tR tR tR tR t	RR	 lt
R
tV tR# )Úrecipinvgauss_geni%  a}  A reciprocal inverse Gaussian continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `recipinvgauss` is:

.. math::

    f(x, \mu) = \frac{1}{\sqrt{2\pi x}}
                \exp\left(\frac{-(1-\mu x)^2}{2\mu^2x}\right)

for :math:`x \ge 0`.

`recipinvgauss` takes ``mu`` as a shape parameter for :math:`\mu`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r  rj   rl   s   &r5   rm   Úrecipinvgauss_gen._shape_info*%  r5  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  rˆ  s   &&&r5   ru   Úrecipinvgauss_gen._pdf-%  s   € ô �vŠv�d—l‘l 1Ó)Ó*Ð*r7   c                ó^   € \         P                  ! V^ 8„  W3R \        P                  ) R7      # )r   c                 óä   € ^W,          ,
          R,          ) ^V ,          VR,          ,          ,          R\         P                  ! ^\         P                  ,          V ,          4      ,          ,
          # r¶  r  )rt   ry  s   &&r5   r  Ú+recipinvgauss_gen._logpdf.<locals>.<lambda>5%  sD   € ˜Q ¥�X¨�OÐ+¨q°­s°2°sµ7­{Õ;Ø ¤§¢¨¬"¯%©%­°­	Ó!2Õ2ö3r7   r  rU  rˆ  s   &&&r5   rý   Úrecipinvgauss_gen._logpdf2%  s,   € Ü�ŠØ�‰E�A�7ñ4äŸ™�wô	 ð 	 r7   c                ó  € R V,          V,
          pR V,          V,           pR \         P                  ! V4      ,          p\        V) V,          4      \         P                  ! RV,          4      \        V) V,          4      ,          ,
          # rm  ©rQ   r'  rÜ   rÓ   ©rD   rt   ry  Útrm1Útrm2Úisqxs   &&&   r5   ry   Úrecipinvgauss_gen._cdf9%  s_   € Ø�2�v˜�zˆØ�2�v˜�zˆØ”2—7’7˜1“:�~ˆÜ˜$˜˜t�Ó$¤r§v¢v¨c°"­f£~´iÀÀÀdÅ
Ó6KÕ'KÕKÐKr7   c                ó  € R V,          V,
          pR V,          V,           pR \         P                  ! V4      ,          p\        WS,          4      \         P                  ! RV,          4      \        V) V,          4      ,          ,           # rm  r,  r-  s   &&&   r5   r~   Úrecipinvgauss_gen._sf?%  s[   € Ø�2�v˜�zˆØ�2�v˜�zˆØ”2—7’7˜1“:�~ˆÜ˜�Ó#¤b§f¢f¨S°­V£n´YÀ¸uÀT½zÓ5JÕ&JÕJÐJr7   Nc                ó8   € R VP                  VR VR7      ,          # r‚  rƒ  r…  s   &&&&r5   rö   Úrecipinvgauss_gen._rvsE%  s   € Ø�<×$Ñ$ R¨°4Ð$Ó8Õ8Ð8r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r~   rö   r‘   r’   r“   s   @r5   r"  r"  %  s0   ø‡ € ñò,Fò+ò
 òLòK÷9ò 9r7   r"  Úrecipinvgaussc                   óX   a € ] tR tRt o RtR tR tR tR tR t	RR	 lt
R
 tR tRtV tR# )Úsemicircular_geniL%  aÌ  A semicircular continuous random variable.

%(before_notes)s

See Also
--------
rdist

Notes
-----
The probability density function for `semicircular` is:

.. math::

    f(x) = \frac{2}{\pi} \sqrt{1-x^2}

for :math:`-1 \le x \le 1`.

The distribution is a special case of `rdist` with ``c = 3``.

%(after_notes)s

References
----------
.. [1] "Wigner semicircle distribution",
       https://en.wikipedia.org/wiki/Wigner_semicircle_distribution

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úsemicircular_gen._shape_infok%  r¼   r7   c                ó€   € R \         P                  ,          \         P                  ! ^W,          ,
          4      ,          # rr  r#  r¿   s   &&r5   ru   Úsemicircular_gen._pdfn%  s#   € Ø”2—5‘5�yœŸš  1¥3¥›Õ'Ð'r7   c                ó¬   € \         P                  ! ^\         P                  ,          4      R\        P                  ! V) V,          4      ,          ,           # rI  rÃ  r¿   s   &&r5   rý   Úsemicircular_gen._logpdfq%  s0   € Ü�vŠv�aœŸ™•g‹ ¤R§X¢X¨q¨b°­d£^Õ!3Õ3Ð3r7   c                óÒ   € R R\         P                  ,          V\         P                  ! ^W,          ,
          4      ,          \         P                  ! V4      ,           ,          ,           # r¢   )rQ   r  r'  r]  r¿   s   &&r5   ry   Úsemicircular_gen._cdft%  s:   € Ø�3”r—u‘u•9˜a¤§¢¨¨!­#­£Õ.´·²¸1³Õ=Õ>Õ>Ð>r7   c                ó.   € \         P                  V^4      # r¥  )r�  r„   rÉ   s   &&r5   r„   Úsemicircular_gen._ppfw%  s   € Ü�z‰z˜!˜QÓÐr7   Nc                óÔ   € \         P                  ! VP                  VR 7      4      p\         P                  ! \         P                  VP                  VR 7      ,          4      pW4,          # rà  )rQ   r'  r´  rQ  r  )rD   rô   rõ   rI  r˜   s   &&&  r5   rö   Úsemicircular_gen._rvsz%  sL   € ô �GŠG�L×(Ñ(¨dÐ(Ó3Ó4ˆÜ�FŠF”2—5‘5˜<×/Ñ/°TÐ/Ó:Õ:Ó;ˆØ�uˆr7   c                ó   € R# )r   )r   r¼  r   r›  r‹   rl   s   &r5   r   Úsemicircular_gen._stats�%  r,  r7   c                ó   € R # )gzCÏ‘ ¡ä?r‹   rl   s   &r5   r  Úsemicircular_gen._entropy„%  s   € Ù%r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   rö   r   r  r‘   r’   r“   s   @r5   r8  r8  L%  s7   ø‡ € ñò<ò(ò4ò?ò ôò ÷&ð &r7   r8  Úsemicircularc                   óR   a € ] tR tRt o RtR tR tR tR tR t	RR lt
R	 tR
tV tR# )Úskewcauchy_geni‹%  a¢  A skewed Cauchy random variable.

%(before_notes)s

See Also
--------
cauchy : Cauchy distribution

Notes
-----

The probability density function for `skewcauchy` is:

.. math::

    f(x) = \frac{1}{\pi \left(\frac{x^2}{\left(a\, \text{sign}(x) + 1
                                               \right)^2} + 1 \right)}

for a real number :math:`x` and skewness parameter :math:`-1 < a < 1`.

When :math:`a=0`, the distribution reduces to the usual Cauchy
distribution.

%(after_notes)s

References
----------
.. [1] "Skewed generalized *t* distribution", Wikipedia
   https://en.wikipedia.org/wiki/Skewed_generalized_t_distribution#Skewed_Cauchy_distribution

%(example)s

c                ó4   € \         P                  ! V4      ^8  # r_   )rQ   r	  rG  s   &&r5   rd   Úskewcauchy_gen._argcheck­%  s   € Ü�vŠv�a‹y˜1‰}Ðr7   c                ó    € \        R RRR4      .# )r˜   F)r›  r–   r4  ©r   rl   s   &r5   rm   Úskewcauchy_gen._shape_info°%  s   € Ü˜3  {°NÓCÐDÐDr7   c                óº   € ^\         P                  V^,          V\         P                  ! V4      ,          ^,           ^,          ,          ^,           ,          ,          # r_   )rQ   r  rR   r9  s   &&&r5   ru   Úskewcauchy_gen._pdf³%  s:   € Ø”B—E‘E˜Q �T Q¬¯ª°«¥^°aÕ%7¸!Õ$;Õ;¸aÕ?Õ@ÕAÐAr7   c                ó   € \         P                  ! V^ 8*  ^V,
          ^,          ^V,
          \         P                  ,          \         P                  ! V^V,
          ,          4      ,          ,           ^V,
          ^,          ^V,           \         P                  ,          \         P                  ! V^V,           ,          4      ,          ,           4      # r  )rQ   r±  r  rÜ  r9  s   &&&r5   ry   Úskewcauchy_gen._cdf¶%  s   € Ü�xŠx˜˜Q™Ø˜Q� !� q¨1¥u´·±¥o¼¿	º	À!ÀqÈ1ÅuÅ+Ó8NÕ&NÕNØ˜Q� !� q¨1¥u´·±¥o¼¿	º	À!ÀqÈ1ÅuÅ+Ó8NÕ&NÕNóPð 	Pr7   c           
     óÂ  € WP                  ^ V4      8  p\        P                  ! V\        P                  ! \        P                  ^V,
          ,          V^V,
          ^,          ,
          ,          4      ^V,
          ,          \        P                  ! \        P                  ^V,           ,          V^V,
          ^,          ,
          ,          4      ^V,           ,          4      # r  )ry   rQ   r±  rÉ  r  )rD   rt   r˜   rS  s   &&& r5   r„   Úskewcauchy_gen._ppf»%  s�   € Ø—	‘	˜!˜Q“ÑˆÜ�xŠx˜ÜŸšœrŸu™u¨¨A­�°!°q¸1µuÀµkµ/ÕBÓCÀqÈ1ÅuÕMÜŸšœrŸu™u¨¨A­�°!°q¸1µuÀµkµ/ÕBÓCÀqÈ1ÅuÕMóOð 	Or7   c                ó~   € \         P                  \         P                  \         P                  \         P                  3# rO   r  )rD   r˜   rl  s   &&&r5   r   Úskewcauchy_gen._statsÁ%  r  r7   c                óª   € \        V\        4      '       d   VP                  4       p\        P                  ! V. RO4      w  r#pRW4V,
          ^,          3# )r"  r•   r#  r&  )rD   rE   r)  r*  r+  s   &&   r5   r×  Úskewcauchy_gen._fitstartÄ%  sD   € ô �dœL×)Ò)Ø—>‘>Ó#ˆDÜŸš dªLÓ9‰ˆ�#Ø�C �) Q�Ð&Ð&r7   r‹   Nry  )rŒ   r�   rŽ   r�   r�   rd   rm   ru   ry   r„   r   r×  r‘   r’   r“   s   @r5   rK  rK  ‹%  s7   ø‡ € ñ òBòEòBòPò
Oô.÷'ð 'r7   rK  Ú
skewcauchyc                   ó°   a a€ ] tR tRt oRtR tR tR tR tV 3R lt	R t
R	 tR
 tRR ltRR lt]R 4       tR t]! ]RR7      V 3R l4       tRtVtV ;t# )Úskewnorm_geniÑ%  aõ  A skew-normal random variable.

%(before_notes)s

Notes
-----
The pdf is::

    skewnorm.pdf(x, a) = 2 * norm.pdf(x) * norm.cdf(a*x)

`skewnorm` takes a real number :math:`a` as a skewness parameter
When ``a = 0`` the distribution is identical to a normal distribution
(`norm`). `rvs` implements the method of [1]_.

This distribution uses routines from the Boost Math C++ library for
the computation of ``cdf``, ``ppf`` and ``isf`` methods. [2]_

%(after_notes)s

References
----------
.. [1] A. Azzalini and A. Capitanio (1999). Statistical applications of
    the multivariate skew-normal distribution. J. Roy. Statist. Soc.,
    B 61, 579-602. :arxiv:`0911.2093`
.. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

%(example)s

c                ó.   € \         P                  ! V4      # rO   rÅ  rG  s   &&r5   rd   Úskewnorm_gen._argcheckï%  rÇ  r7   c                ó^   € \        R R\        P                  ) \        P                  3R4      .# r3  rj   rl   s   &r5   rm   Úskewnorm_gen._shape_infoò%  rÊ  r7   c                ó@   € \         P                  ! V^ 8H  W3R R 4      # )r   c                 ó   € \        V 4      # rO   rù   ©rt   r˜   s   &&r5   r  Ú#skewnorm_gen._pdf.<locals>.<lambda>ø%  s   € œ 1œr7   c                 óR   € R \        V 4      ,          \        W,          4      ,          # rr  rn  rd  s   &&r5   r  re  ù%  s   € ˜œI a›L�¬°1µ3«Ö7r7   r=  r9  s   &&&r5   ru   Úskewnorm_gen._pdfõ%  s$   € Ü�ŠØ�‰F�Q�FÙ%Ù7ó9ð 	9r7   c                ó@   € \         P                  ! V^ 8H  W3R R 4      # )r   c                 ó   € \        V 4      # rO   rü   rd  s   &&r5   r  Ú&skewnorm_gen._logpdf.<locals>.<lambda>þ%  s   € œ aœr7   c                 óz   € \         P                  ! ^4      \        V 4      ,           \        W,          4      ,           # rD  r[  rd  s   &&r5   r  rj  ÿ%  s!   € œŸš ›¤<°£?Õ2´<ÀÅÓ3DÖDr7   r=  r9  s   &&&r5   rý   Úskewnorm_gen._logpdfû%  s&   € Ü�ŠØ�‰F�Q�FÙ(ÙDóFð 	Fr7   c                ó,  <€ \         P                  ! V4      p\        P                  ! VR RV4      p\         P                  ! W#P
                  4      pVR8  V^ 8„  ,          p\        SV `  W,          W$,          4      W4&   \         P                  ! V^ ^4      # )r•   r–   g�íµ ÷Æ°>)	rQ   ré  rq   Ú_skewnorm_cdfrv  rG  r@   ry   rž  )rD   rt   r˜   r¯   Úi_small_cdfrØ  s   &&&  €r5   ry   Úskewnorm_gen._cdf&  su   ø€ Ü�MŠM˜!ÓˆÜ×Ò  3¨¨QÓ/ˆä�OŠO˜AŸy™yÓ)ˆà˜T‘z a¨!¡eÕ,ˆÜ ™7™<¨­¸½ÓGˆÑÜ�wŠw�s˜A˜qÓ!Ð!r7   c                ó4   € \         P                  ! VR RV4      # ©r•   r–   )rq   Ú_skewnorm_ppfr9  s   &&&r5   r„   Úskewnorm_gen._ppf&  ó   € Ü× Ò   C¨¨aÓ0Ð0r7   c                ó*   € V P                  V) V) 4      # rO   r×	  r9  s   &&&r5   r~   Úskewnorm_gen._sf&  s   € ð �y‰y˜!˜˜a˜RÓ Ð r7   c                ó4   € \         P                  ! VR RV4      # rr  )rq   Ú_skewnorm_isfr9  s   &&&r5   rˆ   Úskewnorm_gen._isf&  ru  r7   c                óF  € VP                  VR 7      pVP                  VR 7      pV\        P                  ! ^V^,          ,           4      ,          pWd,          V\        P                  ! ^V^,          ,
          4      ,          ,           p\        P                  ! V^ 8¬  Ww) 4      # rà  )rá  rQ   r'  r±  )rD   r˜   rô   rõ   Úu0r  r  r*  s   &&&&    r5   rö   Úskewnorm_gen._rvs&  s|   € Ø× Ñ  dÐ Ó+ˆØ×Ñ TÐÓ*ˆØŒb�gŠg�a˜!˜Q�$•hÓÕˆØ�T�A”b—g’g˜a ! Q¥$�hÓ'Õ'Õ'ˆÜ�xŠx˜˜a™  SÓ)Ð)r7   c                óp  € . ROp\         P                  ! ^\         P                  ,          4      V,          \         P                  ! ^V^,          ,           4      ,          pRV9   d   WC^ &   RV9   d   ^V^,          ,
          V^&   RV9   dY   ^\         P                  ,
          ^,          V\         P                  ! ^V^,          ,
          4      ,          ^,          ,          V^&   RV9   dL   ^\         P                  ^,
          ,          V^,          ^V^,          ,
          ^,          ,          ,          V^&   V# )Nrì  r  rj  rk  rï  r)  )rD   r˜   rl  r…  Úconsts   &&&  r5   r   Úskewnorm_gen._stats&  sÖ   € Ú)ˆÜ—’˜œ"Ÿ%™%�Ó  1Õ$¤R§W¢W¨Q°°Aµ­XÓ%6Õ6ˆà�'Œ>Ø�1‰IØ�'Œ>Ø˜E 1�H�ˆF�1‰IØ�'Œ>ØœbŸe™e�) Q�¨5´·²¸¸UÀA½X½Ó1FÕ+FÈÕ*JÕJˆF�1‰IØ�'Œ>ØœBŸE™E A�I�¨5°!­8°Q¸À½µ\ÀAÕ4EÕ+EÕFˆF�1‰Iàˆr7   c                ó  € ^\        ^.4      ^\        ^R.4      ^\        . RO4      ^\        . RO4      ^	\        . RO4      ^\        . RO4      ^\        . RO4      ^\        . RO4      ^\        . RO4      ^\        . R	O4      /
pV# )
rM   r  )é   iöÿÿÿr¦  )éi   i—ÿÿÿé?   iñÿÿÿ)i±  iûÿÿin  iäýÿÿrƒ  )é›(  iS¼ÿÿi6Q  iþÅÿÿi�  iOüÿÿ)iß iBàûÿi�/ iÌúÿiÉo iàþÿr…  )éî iƒÔ·ÿiáç� i«Yeÿi{Hx i±óÄÿi“§ i!ðýÿ)	i!Ïi¨×…úiì‡€iø†‘ïiV ùiX'‹õiƒliˆ‘çþr†  )
is_'i§áìŠl   </õ1 lýÿÿÿdy˜( l   J8²D lýÿÿÿ.~ l   ¬-Rx iìW¢i[©iß0òýr   )rD   Úskewnorm_odd_momentss   & r5   Ú_skewnorm_odd_momentsÚ"skewnorm_gen._skewnorm_odd_moments2&  s–   € ð Œz˜1˜#‹ØŒz˜1˜b˜'Ó"ØŒzš,Ó'ØŒzÒ.Ó/ØŒzÒ7Ó8Ø”
ÒEÓFØ”
ò #ó $à”
ò 8ó 9à”
ò %ó &ð ”
ò 2ó 3ð 
Ðð$ $Ð#r7   c                ó„  € V^,          '       do   V^8”  d   \        R4      hV\        P                  ! ^V^,          ,           4      ,          pW0P                  V,          ! V^,          4      ,          \        ,          # \
        P                  ! V^,           ^,          4      ^V^,          ,          ,          \        ,          # )rÑ   zKskewnorm noncentral moments not implemented for odd orders greater than 19.)r  rQ   r'  rˆ  r&   r|   r(  r%   )rD   r/  r˜   r6	  s   &&& r5   r,  Úskewnorm_gen._munpH&  s“   € Ø�1�9Œ9Ø�rŒzÜ)ð +5ó 6ð 6ð
 ”b—g’g˜a ! Q¥$�hÓ'Õ'ˆEØ×6Ñ6°uÖ=¸eÀQ½hÓGÕGÜ%õ&ð 'ô —8’8˜U Q�Y¨�MÓ*¨Q°°qµ­\Õ9¼HÕDÐDr7   aÕ          If ``method='mm'``, parameters fixed by the user are respected, and the
        remaining parameters are used to match distribution and sample moments
        where possible. For example, if the user fixes the location with
        ``floc``, the parameters will only match the distribution skewness and
        variance to the sample skewness and variance; no attempt will be made
        to match the means or minimize a norm of the errors.
        Note that the maximum possible skewness magnitude of a
        `scipy.stats.skewnorm` distribution is approximately 0.9952717; if the
        magnitude of the data's sample skewness exceeds this, the returned
        shape parameter ``a`` will be infinite.
        

r  c           
     óB  <€ VP                  R R4      '       d   \        SV `  ! V.VO5/ VB # \        V\        4      '       d;   VP                  4       ^ 8X  d   VP                  4       pM\        SV `  ! V.VO5/ VB # \        WW#4      w  rrVVP                  RR4      P                  4       pR pR p	VR8X  d   RRRrËp
M@\        V4      '       d
   V^ ,          MRp
VP                  RR4      pVP                  R	R4      pVfç   V
fã   \        P                  ! V4      pVR8X  d   \        P                  ! VRR
4      pM V! ^4      p\        P                  ! WÞ) V4      pV	! V4      p\        P                  ! RR7      ;_uu_ 4        \        P                   ! \        P"                  ! V^,          ^V^,          ,
          4      4      \        P$                  ! V4      ,          p
RRR4       M3Ve   TMT
p
V
\        P                   ! ^V
^,          ,           4      ,          pVfc   Vf_   \        P&                  ! V4      p\        P                   ! V^^V^,          ,          \        P(                  ,          ,
          ,          4      pMVe   TpVf[   VfW   \        P*                  ! V4      pVWÏ,          \        P                   ! ^\        P(                  ,          4      ,          ,
          pMVe   TpVR8X  d   W«V3# \        SV `  ! W3RVR	V/VB #   + '       g   i     EL; i)rE  Fr0   r:   c                 ó*  € ^\         P                  ,
          ^,          V \         P                  ! ^\         P                  ,          4      ,          ^,          ^^V ^,          ,          \         P                  ,          ,
          R,          ,          ,          # r¨  r#  ©r  s   &r5   Úskew_dÚ skewnorm_gen.fit.<locals>.skew_dy&  s]   € Ø”b—e‘e•G˜Q•; 1¤r§w¢w¨q´2·5±5­yÓ'9Õ#9¸AÕ"=Ø%&¨¨1¨a­4­´"·%±%­Õ%7¸3Õ$?õ#@õ Að Ar7   c                 ó8  € \         P                  ! V 4      R,          p\         P                  ! V 4      \         P                  ! \         P                  ^,          V,          V^\         P                  ,
          ^,          R,          ,           ,          4      ,          # )rÑ   rv  )rQ   r	  rR   r'  r  )rL  Ús_23s   & r5   Úd_skewÚ skewnorm_gen.fit.<locals>.d_skew}&  s^   € Ü—6’6˜$“< #Õ&ˆDÜ—7’7˜4“=¤2§7¢7Ü—‘�a•˜$• $¨1¬r¯u©u­9°a­-¸3Õ)?Õ"?Õ@ó$õ ð r7   r;   Nr-   r.   g®Gáz®ï?rl  rm  g®Gáz®ï¿)r2   r@   rB   r>   r)   r?   rÕ  rR  r<   r=   rç  rF  rL  rQ   rž  ro  r'  rn  rR   rê  r  r&  )rD   rE   rF   r4   rà  r  r  r0   r�  r“  r˜   r-   r.   rj  Ús_maxr  r  rì  rØ  s   &&*,              €r5   rB   Úskewnorm_gen.fit\&  sˆ  ø€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3Ü�dœL×)Ò)Ø× Ñ Ó" aÔ'Ø—~‘~Ó'‘ä‘w’{ 4Ð7¨$Ò7°$Ñ7Ð7ô "=¸TØ=Aó"IÑˆ�$à—‘˜( EÓ*×0Ñ0Ó2ˆò	Aò	ð �TŒ>Ø  $¨�EˆA�Eä˜tŸ9š9��Q–¨$ˆAØ—(‘(˜5 $Ó'ˆCØ—H‘H˜W dÓ+ˆEàŠ:˜!š)ô —
’
˜4Ó ˆAØ˜Œô —G’G˜A˜u dÓ+‘á˜q›	�Ü—G’G˜A˜v uÓ-�Ù�q“	ˆAÜ—’ H×-Ö-Ü—G’GœBŸIšI a¨¥d¨Q¨q°!­t­VÓ5Ó6´r·w²w¸q³zÕA�÷ .Ð-ð ’n‘¨!ˆAØ”B—G’G˜A  1¥�HÓ%Õ%ˆAàŠ>˜ešmÜ—’�t“ˆAÜ—G’G˜A  Q q¨!¥t¥V¬B¯E©E¥\Õ!1Õ2Ó3‰EØÒØˆEàŠ<˜CšKÜ—’˜“ˆAØ�e•gœbŸgšg a¬¯©¥gÓ.Õ.Õ.‰CØÒØˆCà�TŒ>Ø˜5�=Ð ô ‘7’;˜tÑE¨CÐE°uÐEÀÑEÐE÷/ .×-Ð-ús   ÆALÌL	r‹   r.  ry  )rŒ   r�   rŽ   r�   r�   rd   rm   ru   rý   ry   r„   r~   rˆ   rö   r   r   rˆ  r,  r	   r   rB   r‘   r’   r  r   s   @@r5   r]  r]  Ñ%  sƒ   ù‡ € ñò:òKò9òFõ"ò1ò!ò
1ô*ôð* ñ$ó ð$ò*Eñ( ˜}ð 5ô ôGFó÷GFð GFr7   r]  Úskewnormc                   ód   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tRV 3R
 lltRtVtV ;t# )Útrapezoid_geniµ&  a?  A trapezoidal continuous random variable.

%(before_notes)s

Notes
-----
The trapezoidal distribution can be represented with an up-sloping line
from ``loc`` to ``(loc + c*scale)``, then constant to ``(loc + d*scale)``
and then downsloping from ``(loc + d*scale)`` to ``(loc+scale)``.  This
defines the trapezoid base from ``loc`` to ``(loc+scale)`` and the flat
top from ``c`` to ``d`` proportional to the position along the base
with ``0 <= c <= d <= 1``.  When ``c=d``, this is equivalent to `triang`
with the same values for `loc`, `scale` and `c`.
The method of [1]_ is used for computing moments.

`trapezoid` takes :math:`c` and :math:`d` as shape parameters.

%(after_notes)s

The standard form is in the range [0, 1] with c the mode.
The location parameter shifts the start to `loc`.
The scale parameter changes the width from 1 to `scale`.

%(example)s

References
----------
.. [1] Kacker, R.N. and Lawrence, J.F. (2007). Trapezoidal and triangular
   distributions for Type B evaluation of standard uncertainty.
   Metrologia 44, 117-127. :doi:`10.1088/0026-1394/44/2/003`


c                óZ   € V^ 8¬  V^8*  ,          V^ 8¬  ,          V^8*  ,          W!8¬  ,          # r  r‹   ©rD   r\  r  s   &&&r5   rd   Útrapezoid_gen._argcheck×&  s.   € Ø�Q‘˜1 ™6Õ" a¨1¡fÕ-°°a±Õ8¸A¹FÕCÐCr7   c                ó@   € \        R RRR4      p\        RRRR4      pW.# )r\  Fr  r  ©TTrO  rx  s   &  r5   rm   Útrapezoid_gen._shape_infoÚ&  s)   € Ü˜˜U H¨lÓ;ˆÜ˜˜U H¨lÓ;ˆØˆxˆr7   c                ó|   € ^W2,
          ^,           ,          p\        W8  W!8*  W8*  ,          W8„  .R R R .WW434      # )rÑ   c                 ó    € W0,          V,          # rO   r‹   ©rt   r\  r  rµ  s   &&&&r5   r  Ú$trapezoid_gen._pdf.<locals>.<lambda>å&  s
   € ¨q­u°q®yr7   c                 ó   € V# rO   r‹   r¢  s   &&&&r5   r  r£  æ&  s   € ©qr7   c                 ó>   € V^V ,
          ,          ^V,
          ,          # r_   r‹   r¢  s   &&&&r5   r  r£  ç&  s   € ¨q°A°aµC­y¸A¸a½CÖ/@r7   r   )rD   rt   r\  r  rµ  s   &&&& r5   ru   Útrapezoid_gen._pdfß&  sR   € Ø�•�Q•�Kˆä˜A™EØ™V¨©Õ/Ø™Eð#ñ 9Ù0Ù@ðBð  !˜<ó)ð 	)r7   c                óP   € \        W8  W!8*  W8*  ,          W8„  .R  R R .WV34      # )c                 óJ   € V ^,          V,          W!,
          ^,           ,          # rD  r‹   ©rt   r\  r  s   &&&r5   r  Ú$trapezoid_gen._cdf.<locals>.<lambda>î&  s   € ¨A¨q­D°1­H¸½¸A½Ö,>r7   c                 óV   € V^W,
          ,          ,           W!,
          ^,           ,          # rD  r‹   r©  s   &&&r5   r  rª  ï&  s   € ¨Q°°aµcµ­]¸q½sÀ1½uÖ,Er7   c                 ót   € ^^V ,
          ^,          W!,
          ^,           ,          ^V,
          ,          ,
          # r_   r‹   r©  s   &&&r5   r  rª  ð&  s/   € ¨A°°!µ¸­zØ23µ#°aµ%õ09Ø<=¸a½Cõ0Aö -Br7   r   rŽ  s   &&&&r5   ry   Útrapezoid_gen._cdfê&  sF   € Ü˜A™EØ™V¨©Õ/Ø™Eð#ñ ?ÙEñBðCð  !˜9ó&ð 	&r7   c                óÎ  € V P                  W"V4      V P                  W2V4      rTW8  W8*  W8„  .p\        P                  ! W,          ^V,           V,
          ,          4      RV,          ^V,           V,
          ,          RV,          ,           ^\        P                  ! ^V,
          W2,
          ^,           ,          ^V,
          ,          4      ,
          .p\        P                  ! Wg4      # r 	  )ry   rQ   r'  Úselect)rD   rƒ   r\  r  ÚqcÚqdr]  r‚  s   &&&&    r5   r„   Útrapezoid_gen._ppfô&  s«   € Ø—‘˜1 Ó# T§Y¡Y¨q°QÓ%7ˆBØ‘F˜A™G Q¡VÐ,ˆÜ—g’g˜a�e q¨1¥u¨q¥yÕ1Ó2Ø˜A•g  Q¥¨¥Õ+¨c°A­gÕ5Øœ"Ÿ'š' 1 q¥5¨Q­U°Q­YÕ"7¸1¸q½5Õ"AÓBÕBðDˆ
ô �yŠy˜Ó.Ð.r7   c                ó  a€ VS^,           ,          p\        VR8H  RV8  VR8  ,          VR8H  .R V3R lV3R l.V.4      pRRV,           V,
          ,          WT,
          ,          S^,           S^,           ,          ,          pV# )rM   r•   r–   c                 ó   € R # r8  r‹   rŽ  s   &r5   r  Ú%trapezoid_gen._munp.<locals>.<lambda>'  s   € ‘sr7   c                 ó�   <€ \         P                  ! S^,           \         P                  ! V 4      ,          4      V R,
          ,          # r"
  )rQ   rf  r  ©r  rc   s   &€r5   r  rµ  '  s(   ø€ ”r—x’x  1¥¬¯ª¨q«	Õ 1Ó2°a¸µeÖ<r7   c                 ó   <€ S^,           # rD  r‹   r·  s   &€r5   r  rµ  '  s	   ø€ �q˜–sr7   rÒ   r   )rD   rc   r\  r  Úab_termÚdc_termr˜  s   &f&&   r5   r,  Útrapezoid_gen._munpü&  s�   ø€ ð �a˜•c•(ˆÜØ�#‰X˜˜a™ A¨¡GÕ,¨a°3©hÐ7ÙÜ<Üðð ˆCóˆð �S˜•U˜1•W�o Õ!2Õ3¸¸!½ÀÀ!Åµ}ÕEˆØˆ
r7   c                óº   € R RV,
          V,           ,          RV,           V,
          ,          \         P                  ! R RV,           V,
          ,          4      ,           # r¢   rc  r›  s   &&&r5   r  Útrapezoid_gen._entropy'  s=   € ð �c˜!•e˜A•g� # a¥%¨¥'Õ*¬R¯VªV°C¸3¸q½5À½7µOÓ-DÕDÐDr7   c                ó0   <€ Vf   Rp\         SV `  WR7      # )Nr…  )g…ëQ¸Õ?g…ëQ¸å?ra  r\	  s   &&&€r5   r×  Útrapezoid_gen._fitstart'  s    ø€ àŠ<ØˆDÜ‰wÑ  Ð Ó1Ð1r7   r‹   rO   )rŒ   r�   rŽ   r�   r�   rd   rm   ru   ry   r„   r,  r  r×  r‘   r’   r  r   s   @@r5   r™  r™  µ&  s:   ù‡ € ñ òBDòò
	)ò&ò/òò2E÷2÷ 2r7   r™  Ú	trapezoidc                   óX   a € ] tR tRt o RtRR ltR tR tR tR t	R	 t
R
 tR tRtV tR# )Ú
triang_geni('  a  A triangular continuous random variable.

%(before_notes)s

Notes
-----
The triangular distribution can be represented with an up-sloping line from
``loc`` to ``(loc + c*scale)`` and then downsloping for ``(loc + c*scale)``
to ``(loc + scale)``.

`triang` takes ``c`` as a shape parameter for :math:`0 \le c \le 1`.

%(after_notes)s

The standard form is in the range [0, 1] with c the mode.
The location parameter shifts the start to `loc`.
The scale parameter changes the width from 1 to `scale`.

%(example)s

Nc                ó*   € VP                  ^ V^V4      # r  )Ú
triangularrÖ  s   &&&&r5   rö   Útriang_gen._rvs>'  s   € Ø×&Ñ& q¨!¨Q°Ó5Ð5r7   c                ó    € V^ 8¬  V^8*  ,          # r  r‹   r÷  s   &&r5   rd   Útriang_gen._argcheckA'  s   € Ø�Q‘˜1 ™6Õ"Ð"r7   c                ó    € \        R RRR4      .# )r\  Fr  rž  rO  rl   s   &r5   rm   Útriang_gen._shape_infoD'  s   € Ü˜3  x°Ó>Ð?Ð?r7   c                ób   € \        V^ 8H  W8  W8¬  V^8g  ,          V^8H  .R R R R .W34      pV# )r   c                 ó"   € ^^V ,          ,
          # rD  r‹   rÔ  s   &&r5   r  Ú!triang_gen._pdf.<locals>.<lambda>Q'  s   €  a¨!¨a­%¦ir7   c                 ó"   € ^V ,          V,          # rD  r‹   rÔ  s   &&r5   r  rÌ  R'  s   €  a¨!¥e¨a¦ir7   c                 ó>   € ^^V ,
          ,          ^V,
          ,          # rD  r‹   rÔ  s   &&r5   r  rÌ  S'  s   €  a¨1¨q­5¥k°Q¸µUÖ&;r7   c                 ó   € ^V ,          # rD  r‹   rÔ  s   &&r5   r  rÌ  T'  s   €  a¨!¦er7   r   ©rD   rt   r\  rI  s   &&& r5   ru   Útriang_gen._pdfG'  sT   € ô ˜˜a™Ø™Ø™& Q¨!¡VÕ,Ø˜a™ð!ñ 0Ù/Ù;Ù+ð-ð ˜ó ˆð ˆr7   c                ób   € \        V^ 8H  W8  W8¬  V^8g  ,          V^8H  .R R R R .W34      pV# )r   c                 ó.   € ^V ,          W ,          ,
          # rD  r‹   rÔ  s   &&r5   r  Ú!triang_gen._cdf.<locals>.<lambda>]'  s   €  a¨¥c¨A­C¦ir7   c                 ó    € W ,          V,          # rO   r‹   rÔ  s   &&r5   r  rÔ  ^'  s
   €  a¥e¨a¦ir7   c                 óX   € W ,          ^V ,          ,
          V,           V^,
          ,          # rD  r‹   rÔ  s   &&r5   r  rÔ  _'  s   €  q¥s¨Q¨q­S¥y°1¥}¸¸1½Ö&=r7   c                 ó   € W ,          # rO   r‹   rÔ  s   &&r5   r  rÔ  `'  s   €  a¦er7   r   rÐ  s   &&& r5   ry   Útriang_gen._cdfX'  sR   € Ü˜˜a™Ø™Ø™& Q¨!¡VÕ,Ø˜a™ð!ñ 0Ù/Ù=Ù+ð-ð ˜ó ˆð ˆr7   c           
     óÊ   € \         P                  ! W8  \         P                  ! W!,          4      ^\         P                  ! ^V,
          ^V,
          ,          4      ,
          4      # r_   )rQ   r±  r'  rg  s   &&&r5   r„   Útriang_gen._ppfd'  s;   € Ü�xŠx˜™œrŸwšw q¥u›~¨q´·²¸!¸A½#À!ÀAÅ#½Ó1GÕ/GÓHÐHr7   c           	     óX  € VR ,           R,          R V,
          W,          ,           ^,          \         P                  ! ^4      ^V,          ^,
          ,          V^,           ,          V^,
          ,          ^\         P                  ! R V,
          W,          ,           R4      ,          ,          R3# )r–   r£  rS  g333333ã¿)rQ   r'  rU  r÷  s   &&r5   r   Útriang_gen._statsg'  st   € Ø�3•˜•Ø�Q•�q•s•˜B•Ü—’˜“
˜A˜a�C �EÕ" A a¥CÕ(¨!¨A­#Õ.°!´B·H²H¸cÀ!½eÀAÅC½iÈ#Ó4NÕ2NÕOØðð 	r7   c                ó<   € R \         P                  ! ^4      ,
          # r  rc  r÷  s   &&r5   r  Útriang_gen._entropym'  s   € Ø”2—6’6˜!“9�}Ðr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rö   rd   rm   ru   ry   r„   r   r  r‘   r’   r“   s   @r5   rÂ  rÂ  ('  s9   ø‡ € ñô*6ò#ò@òò"
òIò÷ð r7   rÂ  Útriangc                   ól   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 tR
 tV 3R ltR tRtVtV ;t# )Útruncexpon_genit'  a8  A truncated exponential continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `truncexpon` is:

.. math::

    f(x, b) = \frac{\exp(-x)}{1 - \exp(-b)}

for :math:`0 <= x <= b`.

`truncexpon` takes ``b`` as a shape parameter for :math:`b`.

%(after_notes)s

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# r”  rj   rl   s   &r5   rm   Útruncexpon_gen._shape_infoŠ'  r6  r7   c                ó   € V P                   V3# rO   r�  rÀ  s   &&r5   r¥   Útruncexpon_gen._get_support�'  ó   € Ø�v‰v�qˆyÐr7   c                ój   € \         P                  ! V) 4      \        P                  ! V) 4      ) ,          # rO   r¡  r—  s   &&&r5   ru   Útruncexpon_gen._pdf�'  s#   € ä�vŠv�q�b‹zœBŸHšH a R›L˜=Õ)Ð)r7   c                ój   € V) \         P                  ! \        P                  ! V) 4      ) 4      ,
          # rO   r  r—  s   &&&r5   rý   Útruncexpon_gen._logpdf”'  s$   € Øˆr”B—F’FœBŸHšH a R›L˜=Ó)Õ)Ð)r7   c                óh   € \         P                  ! V) 4      \         P                  ! V) 4      ,          # rO   r=  r—  s   &&&r5   ry   Útruncexpon_gen._cdf—'  s!   € Ü�xŠx˜˜‹|œBŸHšH a R›LÕ(Ð(r7   c                óh   € \         P                  ! V\         P                  ! V) 4      ,          4      ) # rO   )r|   ré  rf  r©  s   &&&r5   r„   Útruncexpon_gen._ppfš'  s"   € Ü—’˜œ2Ÿ8š8 Q B›<�Ó(Ð(Ð(r7   c                ó    € \         P                  ! V) 4      \         P                  ! V) 4      ,
          \        P                  ! V) 4      ,          # rO   r¡  r—  s   &&&r5   r~   Útruncexpon_gen._sf�'  s0   € Ü—’˜�r“
œRŸVšV Q B›ZÕ'¬¯ª°1°"«Õ5Ð5r7   c                ó    € \         P                  ! \         P                  ! V) 4      V\        P                  ! V) 4      ,          ,
          4      ) # rO   )rQ   r  rÓ   r|   rf  r©  s   &&&r5   rˆ   Útruncexpon_gen._isf '  s2   € Ü—’”r—v’v˜q˜b“z A¬¯ª°!°«Õ$4Õ4Ó5Ð5Ð5r7   c                ó¦  <€ V^8X  dJ   ^V^,           \         P                  ! V) 4      ,          ,
          \        P                  ! V) 4      ) ,          # V^8X  dl   ^^RW",          ^V,          ,           ^,           ,          \         P                  ! V) 4      ,          ,
          ,          \        P                  ! V) 4      ) ,          # \        SV `  W4      # r 	  )rQ   rÓ   r|   rf  r@   r,  )rD   rc   r™   rØ  s   &&&€r5   r,  Útruncexpon_gen._munp£'  s•   ø€ ð �Œ6Ø�q˜•sœBŸFšF A 2›JÕ&Õ&¬"¯(ª(°A°2«,¨Õ7Ð7Ø�!ŒVØ�a˜˜Q�S  1¥�W Q�Y�¬¯ª°¨r«
Õ2Õ2Õ3´b·h²hÀ¸r³l°]ÕCÐCô ‘7‘= Ó&Ð&r7   c                óº   € \         P                  ! V4      p\         P                  ! V^,
          4      ^W!R,
          ,          ,           RV,
          ,          ,           # r&  rÍ  )rD   r™   ÚeBs   && r5   r  Útruncexpon_gen._entropy®'  s9   € Ü�VŠV�A‹YˆÜ�vŠv�b˜•d‹|˜Q˜r S¥5�z�\¨C°­FÕ3Õ3Ð3r7   r‹   )rŒ   r�   rŽ   r�   r�   rm   r¥   ru   rý   ry   r„   r~   rˆ   r,  r  r‘   r’   r  r   s   @@r5   rá  rá  t'  sB   ù‡ € ñò*Eòò*ò*ò)ò)ò6ò6õ	'÷4ò 4r7   rá  Ú
truncexponc                 ó4   € \         P                  ! W.^ R7      # )r   rO  )r|   ró  ©Úlog_pÚlog_qs   &&r5   Ú_log_sumrý  ¸'  s   € Ü�<Š<˜˜¨QÔ/Ð/r7   c                 ól   € \         P                  ! W\        P                  R ,          ,           .^ R7      # )ù              ð?rO  )r|   ró  rQ   r  rú  s   &&r5   rÐ  rÐ  ½'  s"   € Ü�<Š<˜¤b§e¡e¨B¥h¥Ð/°aÔ8Ð8r7   c                ó"  a€ \         P                  ! W4      w  rV^ 8*  pV ^ 8„  pW#,          ( pR oV3R lpR p\         P                  ! V \         P                  \         P                  R7      pW,          P
                  '       d   S! W,          W,          4      Wr&   W,          P
                  '       d   V! W,          W,          4      Ws&   W,          P
                  '       d   V! W,          W,          4      Wt&   \         P                  ! V4      # )z3Log of Gaussian probability mass within an intervalc                 ó>   € \        \        V4      \        V 4      4      # rO   )rÐ  rß   rò  s   &&r5   Úmass_case_leftÚ'_log_gauss_mass.<locals>.mass_case_leftË'  s   € Üœ a›¬,°q«/Ó:Ð:r7   c                 ó   <€ S! V) V ) 4      # rO   r‹   )r˜   r™   r  s   &&€r5   Úmass_case_rightÚ(_log_gauss_mass.<locals>.mass_case_rightÎ'  s   ø€ Ù˜q˜b 1 "Ó%Ð%r7   c                 ód   € \         P                  ! \        V 4      ) \        V) 4      ,
          4      # rO   )r|   ré  rÜ   rò  s   &&r5   Úmass_case_centralÚ*_log_gauss_mass.<locals>.mass_case_centralÑ'  s$   € ô �xŠxœ 1›˜¬	°1°"«Õ5Ó6Ð6r7   )r  r	  )rQ   rE  r	  rF  Ú
complex128rô   r  )	r˜   r™   Ú	case_leftÚ
case_rightÚcase_centralr  r  rJ  r  s	   &&      @r5   Ú_log_gauss_massr  Á'  sÎ   ø€ ä×Ò˜qÓ$�D€Að �Q‘€IØ�Q‘€JØÕ+Ð,€Lò;õ&ò7ô �,Š,�q¤R§V¡V´2·=±=Ô
A€CØ…|××ÐÙ'¨­°aµlÓCˆ‰Ø…}××ÐÙ)¨!­-¸½ÓGˆ‰Ø…××ÐÙ-¨a­o¸q½ÓOˆÑÜ�7Š7�3‹<Ðr7   c                   óŽ   a a€ ] tR tRt oRtR tR tV 3R ltR tR t	R t
R	 tR
 tR tR tR tR tR tR tRR ltRtVtV ;t# )Útruncnorm_genié'  a¯	  A truncated normal continuous random variable.

%(before_notes)s

Notes
-----
This distribution is the normal distribution centered on ``loc`` (default
0), with standard deviation ``scale`` (default 1), and truncated at ``a``
and ``b`` *standard deviations* from ``loc``. For arbitrary ``loc`` and
``scale``, ``a`` and ``b`` are *not* the abscissae at which the shifted
and scaled distribution is truncated.

.. note::
    If ``a_trunc`` and ``b_trunc`` are the abscissae at which we wish
    to truncate the distribution (as opposed to the number of standard
    deviations from ``loc``), then we can calculate the distribution
    parameters ``a`` and ``b`` as follows::

        a, b = (a_trunc - loc) / scale, (b_trunc - loc) / scale

    This is a common point of confusion. For additional clarification,
    please see the example below.

%(example)s

In the examples above, ``loc=0`` and ``scale=1``, so the plot is truncated
at ``a`` on the left and ``b`` on the right. However, suppose we were to
produce the same histogram with ``loc = 1`` and ``scale=0.5``.

>>> loc, scale = 1, 0.5
>>> rv = truncnorm(a, b, loc=loc, scale=scale)
>>> x = np.linspace(truncnorm.ppf(0.01, a, b),
...                 truncnorm.ppf(0.99, a, b), 100)
>>> r = rv.rvs(size=1000)

>>> fig, ax = plt.subplots(1, 1)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim(a, b)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Note that the distribution is no longer appears to be truncated at
abscissae ``a`` and ``b``. That is because the *standard* normal
distribution is first truncated at ``a`` and ``b``, *then* the resulting
distribution is scaled by ``scale`` and shifted by ``loc``. If we instead
want the shifted and scaled distribution to be truncated at ``a`` and
``b``, we need to transform these values before passing them as the
distribution parameters.

>>> a_transformed, b_transformed = (a - loc) / scale, (b - loc) / scale
>>> rv = truncnorm(a_transformed, b_transformed, loc=loc, scale=scale)
>>> x = np.linspace(truncnorm.ppf(0.01, a, b),
...                 truncnorm.ppf(0.99, a, b), 100)
>>> r = rv.rvs(size=10000)

>>> fig, ax = plt.subplots(1, 1)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim(a-0.1, b+0.1)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
c                ó
   € W8  # rO   r‹   r	  s   &&&r5   rd   Útruncnorm_gen._argcheck*(  s	   € Ø‰uˆr7   c                ó¼   € \        R R\        P                  ) \        P                  3R4      p\        RR\        P                  ) \        P                  3R4      pW.# )r˜   Fr™   ri   )FTrj   r¢  s   &  r5   rm   Útruncnorm_gen._shape_info-(  sG   € Ü˜˜U¤b§f¡f W¬b¯f©fÐ$5°}ÓEˆÜ˜˜U¤b§f¡f W¬b¯f©fÐ$5°}ÓEˆØˆxˆr7   c                óÆ   <€ \        V\        4      '       d   VP                  4       p\        SV `  V\
        P                  ! V4      \
        P                  ! V4      3R 7      # r)	  rÂ  rb  s   &&€r5   r×  Útruncnorm_gen._fitstart2(  sF   ø€ ä�dœL×)Ò)Ø—>‘>Ó#ˆDÜ‰wÑ  ¬R¯VªV°D«\¼2¿6º6À$»<Ð,HÐ ÓIÐIr7   c                ó   € W3# rO   r‹   r	  s   &&&r5   r¥   Útruncnorm_gen._get_support8(  rf  r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r.  r°  s   &&&&r5   ru   Útruncnorm_gen._pdf;(  rÌ  r7   c                ó8   € \        V4      \        W#4      ,
          # rO   )rÙ   r  r°  s   &&&&r5   rý   Útruncnorm_gen._logpdf>(  s   € Ü˜A‹¤°Ó!6Õ6Ð6r7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r  r°  s   &&&&r5   ry   Útruncnorm_gen._cdfA(  rÌ  r7   c           
     óz  € \         P                  ! WV4      w  rp\         P                  ! \        W!4      \        W#4      ,
          4      pVR8„  p\         P                  ! V4      '       dQ   \         P
                  ! \         P                  ! V P                  W,          W%,          W5,          4      4      ) 4      WE&   V# ©çš™™™™™¹?gš™™™™™¹¿)rQ   rE  r#  r  ræ  ré  rÓ   r
  )rD   rt   r˜   r™   ÚlogcdfrS  s   &&&&  r5   r  Útruncnorm_gen._logcdfD(  s   € Ü×%Ò% a¨AÓ.‰ˆˆaÜ—’œO¨AÓ1´OÀAÓ4IÕIÓJˆØ�T‰MˆÜ�6Š6�!�9Š9ÜŸš¤"§&¢&¨¯©°QµT¸1½4ÀÅÓ)FÓ"GÐ!GÓHˆF‰IØˆr7   c                óN   € \         P                  ! V P                  WV4      4      # rO   r“  r°  s   &&&&r5   r~   Útruncnorm_gen._sfL(  r•  r7   c           
     óz  € \         P                  ! WV4      w  rp\         P                  ! \        W4      \        W#4      ,
          4      pVR8„  p\         P                  ! V4      '       dQ   \         P
                  ! \         P                  ! V P                  W,          W%,          W5,          4      4      ) 4      WE&   V# r   )rQ   rE  r#  r  ræ  ré  rÓ   r  )rD   rt   r˜   r™   ÚlogsfrS  s   &&&&  r5   r
  Útruncnorm_gen._logsfO(  s   € Ü×%Ò% a¨AÓ.‰ˆˆaÜ—
’
œ?¨1Ó0´?À1Ó3HÕHÓIˆØ�D‰LˆÜ�6Š6�!�9Š9Ü—x’x¤§¢¨¯©°QµT¸1½4ÀÅÓ(FÓ!GÐ GÓHˆE‰HØˆr7   c                óv  € \        V4      p\        V4      pWC,
          p\        P                  ! \        P                  ! ^\        P                  ,          \        P
                  ,          4      V,          4      pV\        V4      ,          V\        V4      ,          ,
          ^V,          ,          pWg,           pV# rD  )rÜ   rQ   r  r'  r  r	  rÖ   )	rD   r˜   r™   rè  ré  rã  r  ÚDr‰  s	   &&&      r5   r  Útruncnorm_gen._entropyW(  sy   € Ü�a‹LˆÜ�a‹LˆØ�EˆÜ�FŠF”2—7’7˜1œrŸu™u�9¤r§t¡tÕ+Ó,¨qÕ0Ó1ˆØ”˜1“Õ ¤I¨a£LÕ 0Õ0°Q¸µUÕ;ˆØ�EˆØˆr7   c                óJ  € \         P                  ! WV4      w  rpV^ 8  pV( pR pR p\         P                  ! V4      pW,          p	W,          p
V	P                  '       d   V! W’V,          W4,          4      W„&   V
P                  '       d   V! W¢V,          W5,          4      W…&   V# )r   c                 ó    € \        \        V4      \        P                  ! V 4      \	        W4      ,           4      p\
        P                  ! V4      # rO   )rý  rß   rQ   r  r  r|   Ú	ndtri_exp©rƒ   r˜   r™   Ú	log_Phi_xs   &&& r5   Úppf_leftÚ$truncnorm_gen._ppf.<locals>.ppf_leftf(  s7   € Ü ¤¨a£Ü!#§¢¨£¬_¸QÓ-BÕ!BóDˆIä—<’< 	Ó*Ð*r7   c                 ó¦   € \        \        V) 4      \        P                  ! V ) 4      \	        W4      ,           4      p\
        P                  ! V4      ) # rO   )rý  rß   rQ   ré  r  r|   r.  r/  s   &&& r5   Ú	ppf_rightÚ%truncnorm_gen._ppf.<locals>.ppf_rightk(  s?   € Ü ¤¨q¨bÓ!1Ü!#§¢¨1¨"£´ÀÓ0EÕ!EóGˆIä—L’L Ó+Ð+Ð+r7   ©rQ   rE  Ú
empty_likerô   )rD   rƒ   r˜   r™   r  r  r1  r4  rJ  Úq_leftÚq_rights   &&&&       r5   r„   Útruncnorm_gen._ppf`(  s�   € Ü×%Ò% a¨AÓ.‰ˆˆaà˜‘Eˆ	Ø�Zˆ
ò	+ò
	,ô
 �mŠm˜AÓˆà•ˆØ•-ˆà�;�;ˆ;Ù% f°	­l¸A½LÓIˆC‰NØ�<�<ˆ<Ù'¨°:µÀÅÓNˆC‰Oàˆ
r7   c                óJ  € \         P                  ! WV4      w  rpV^ 8  pV( pR pR p\         P                  ! V4      pW,          p	W,          p
V	P                  '       d   V! W’V,          W4,          4      W„&   V
P                  '       d   V! W¢V,          W5,          4      W…&   V# )r   c                 óÈ   € \        \        V4      \        P                  ! V 4      \	        W4      ,           4      p\
        P                  ! \        P                  ! V4      4      # rO   )rÐ  rß   rQ   r  r  r|   r.  r  r/  s   &&& r5   Úisf_leftÚ$truncnorm_gen._isf.<locals>.isf_leftƒ(  s@   € Ü!¤,¨q£/Ü"$§&¢&¨£)¬o¸aÓ.CÕ"CóEˆIä—<’<¤§¢¨	Ó 2Ó3Ð3r7   c                 óÎ   € \        \        V) 4      \        P                  ! V ) 4      \	        W4      ,           4      p\
        P                  ! \        P                  ! V4      4      ) # rO   )rÐ  rß   rQ   ré  r  r|   r.  r  r/  s   &&& r5   Ú	isf_rightÚ%truncnorm_gen._isf.<locals>.isf_rightˆ(  sH   € Ü!¤,°¨rÓ"2Ü"$§(¢(¨A¨2£,´ÀÓ1FÕ"FóHˆIä—L’L¤§¢¨Ó!3Ó4Ð4Ð4r7   r6  )rD   rƒ   r˜   r™   r  r  r=  r@  rJ  r8  r9  s   &&&&       r5   rˆ   Útruncnorm_gen._isf|(  s�   € ä×%Ò% a¨AÓ.‰ˆˆaà˜‘Eˆ	Ø�Zˆ
ò	4ò
	5ô
 �mŠm˜AÓˆà•ˆØ•-ˆà�;�;ˆ;Ù% f°	­l¸A½LÓIˆC‰NØ�<�<ˆ<Ù'¨°:µÀÅÓNˆC‰Oàˆ
r7   c           	     óØ   a € V 3R  lp\         P                  ! V^ 8¬  W"8H  ,          W38H  ,          WV3\        P                  ! V\        P                  .R7      \        P
                  R7      # )c                ó¨  <a€ \         P                  ! W.4      pSP                  W1V4      w  rE\         P                  ! WE) .4      pV^ 8g  p^ ^.p\        ^V ^,           4       Fe  o\        P
                  ! WvV3V3R l^ R7      p	\         P                  ! V	4      S^,
          VR,          ,          ,           p
VP                  V
4       Kg  	  VR,          # )z_
Returns n-th moment. Defined only if n >= 0.
Function cannot broadcast due to the loop over n
c                 ó0   <€ WS^,
          ,          ,          # r_   r‹   )rt   rv  rk  s   &&€r5   r  Ú:truncnorm_gen._munp.<locals>.n_th_moment.<locals>.<lambda>ª(  s   ø€ °A¸A¸a½C½¶Lr7   r  r<  r  )rQ   r#  ru   rR  r  r  rè  r*	  )rc   r˜   r™   ÚabÚpAÚpBÚprobsÚcondrl  rm  Úmkrk  rD   s   &&&        @€r5   Ún_th_momentÚ(truncnorm_gen._munp.<locals>.n_th_momentš(  s´   ù€ ô
 —’˜Q˜FÓ#ˆBØ—Y‘Y˜r aÓ(‰FˆBÜ—J’J  C˜yÓ)ˆEØ˜A‘:ˆDØ˜!�fˆGÜ˜1˜a �c–]�ô
 —’ t°R¨[Ü'@Ø23ô5�ô —V’V˜D“\ Q q¥S¨G°B­KÕ$7Õ7�Ø—‘˜rÖ"ñ #ð ˜2•;Ðr7   r  r  rx	  )rD   rc   r˜   r™   rM  s   f&&& r5   r,  Útruncnorm_gen._munp™(  sP   ø€ õ	ô, �Š  Q¡¨1©6Õ2°a±fÕ=ÀÀa¸yÜ!Ÿ|š|¨KÄÇÁÀÔMÜ*,¯&©&ô2ð 	2r7   c                ó˜   € V P                  \        P                  ! W.4      W4      w  rER  p\        P                  ! V4      pV! WWE4      # )c                 ó¸  € \         P                  ! W.4      pW#,
          pTp\         P                  ! W#) .4      pV^ 8g  p\        P                  ! W‡V3R ^ R7      p	^\         P                  ! V	4      ,           p
\        P                  ! W‡WF,
          3R ^ R7      p	^\         P                  ! V	4      ,           p\        P                  ! W‡V3R ^ R7      p	^V,          \         P                  ! V	4      ,           p\        P                  ! W‡V3R ^ R7      p	^V
,          \         P                  ! V	4      ,           pWÅRV
,          ^V^,          ,          ,           ,          ,           pV\         P
                  ! VR4      ,          pWÕRV,          ^V,          ^V
,          V^,          ,
          ,          ,           ,          ,           pVV^,          ,          ^,
          pWkVV3# )	r   c                 ó   € W,          # rO   r‹   ru  s   &&r5   r  ÚGtruncnorm_gen._stats.<locals>._truncnorm_stats_scalar.<locals>.<lambda>¾(  s   € À1Æ3r7   r  c                 ó   € W,          # rO   r‹   ru  s   &&r5   r  rS  Á(  s   € ÈÎr7   c                 ó    € W^,          ,          # rD  r‹   ru  s   &&r5   r  rS  Æ(  ó
   € À1ÈÅTÆ6r7   c                 ó    € W^,          ,          # r¥  r‹   ru  s   &&r5   r  rS  É(  rV  r7   rS  r_  r`  )rQ   r#  r  r  rè  rU  )r˜   r™   rH  rI  rG  rª  ry  rJ  rK  rm  r«  rz  r¬  Úm4Úmu3r{  Úmu4r|  s   &&&&              r5   Ú_truncnorm_stats_scalarÚ5truncnorm_gen._stats.<locals>._truncnorm_stats_scalar·(  sq  € Ü—’˜Q˜FÓ#ˆBØ•ˆBØˆBä—J’J  C˜yÓ)ˆEØ˜A‘:ˆDÜ—?’? 4°¨Ñ6FØ./ô1ˆDà”R—V’V˜D“\Õ!ˆBÜ—?’? 4°µÐ)9Ñ;KØ./ô1ˆDð ”b—f’f˜T“lÕ"ˆCÜ—?’? 4°¨Ñ6IØ./ô1ˆDà�2•œŸš˜t›Õ$ˆBÜ—?’? 4°¨Ñ6IØ./ô1ˆDà�2•œŸš˜t›Õ$ˆBà˜R �U Q r¨1¥u¥W�_Õ-Õ-ˆCØ”r—x’x  SÓ)Õ)ˆBØ˜2˜b�5 1 R¥4¨¨2­°°Aµ­Õ#6Õ6Õ7Õ7ˆCØ�s˜A•v• Õ!ˆBØ˜B �?Ð"r7   )ÚpdfrQ   r&  r  )rD   r˜   r™   rl  rH  rI  r[  Ú_truncnorm_statss   &&&&    r5   r   Útruncnorm_gen._stats´(  sC   € Ø—‘œ"Ÿ(š( A 6Ó*¨AÓ1‰ˆò	#ô8 Ÿ<š<Ð(?Ó@ÐÙ  bÓ-Ð-r7   r‹   rq  )rŒ   r�   rŽ   r�   r�   rd   rm   r×  r¥   ru   rý   ry   r  r~   r
  r  r„   rˆ   r,  r   r‘   r’   r  r   s   @@r5   r  r  é'  s\   ù‡ € ñ>ò@òõ
Jòò-ò7ò-òò,òòòò8ò:2÷6 .ô  .r7   r  Ú	truncnorm)rš   r·   c                   óÎ   a a€ ] tR tRt oRtR tR tR tR tV 3R lt	R t
R	 tV 3R
 ltR tR tR tV 3R ltR tR tR tR tR t]]! ]4      V 3R l4       4       tRtVtV ;t# )Útruncpareto_geniÛ(  a'  An upper truncated Pareto continuous random variable.

%(before_notes)s

See Also
--------
pareto : Pareto distribution

Notes
-----
The probability density function for `truncpareto` is:

.. math::

    f(x, b, c) = \frac{b}{1 - c^{-b}} \frac{1}{x^{b+1}}

for :math:`b \neq 0`, :math:`c > 1` and :math:`1 \le x \le c`.

`truncpareto` takes `b` and `c` as shape parameters for :math:`b` and
:math:`c`.

Notice that the upper truncation value :math:`c` is defined in
standardized form so that random values of an unscaled, unshifted variable
are within the range ``[1, c]``.
If ``u_r`` is the upper bound to a scaled and/or shifted variable,
then ``c = (u_r - loc) / scale``. In other words, the support of the
distribution becomes ``(scale + loc) <= x <= (c*scale + loc)`` when
`scale` and/or `loc` are provided.

The ``fit`` method assumes that :math:`b` is positive; it does not produce
good results when the data is more consistent with negative :math:`b`.

`truncpareto` can also be used to model a general power law distribution
with PDF:

.. math::

    f(x; a, l, h) = \frac{a}{h^a - l^a} x^{a-1}

for :math:`a \neq 0` and :math:`0 < l < x < h`. Suppose :math:`a`,
:math:`l`, and :math:`h` are represented in code as ``a``, ``l``, and
``h``, respectively. In this case, use `truncpareto` with parameters
``b = -a``, ``c = h / l``, ``scale = l``, and ``loc = 0``.

%(after_notes)s

References
----------
.. [1] Burroughs, S. M., and Tebbens S. F.
    "Upper-truncated power laws in natural systems."
    Pure and Applied Geophysics 158.4 (2001): 741-757.

%(example)s

c                óž   € \        R R\        P                  ) \        P                  3R4      p\        RRR\        P                  3R4      pW.# )r™   Fr\  r–   r4  rj   )rD   r¤  ry  s   &  r5   rm   Útruncpareto_gen._shape_info)  s@   € Ü˜˜U¤b§f¡f W¬b¯f©fÐ$5°~ÓFˆÜ˜˜U S¬"¯&©& M°>ÓBˆØˆxˆr7   c                ó    € VR 8g  VR8„  ,          # rr  r‹   ©rD   r™   r\  s   &&&r5   rd   Útruncpareto_gen._argcheck)  s   € Ø�R‘˜A ™FÕ#Ð#r7   c                ó   € V P                   V3# rO   r�  rf  s   &&&r5   r¥   Útruncpareto_gen._get_support)  ræ  r7   c                ó’   € \        WVR \        R7      w  rpW!V^,           ) ,          ,          ^^W2,          ,          ,
          ,          # ©T©Úforce_floatingÚxp©r   rQ   ©rD   rt   r™   r\  s   &&&&r5   ru   Útruncpareto_gen._pdf)  s7   € ä˜Q 1°T¼bÔA‰ˆˆaØ˜˜!��f•9�}  A a¥d¥F¥
Õ+Ð+r7   c                ó�   <€ \        WVR \        R7      w  rp\        P                  ! V^ 8„  WV3V P                  \
        SV `  4      # rk  )r   rQ   r  r  Ú_logpdf_pos_br@   rý   ©rD   rt   r™   r\  rØ  s   &&&&€r5   rý   Útruncpareto_gen._logpdf$)  ó>   ø€ Ü˜Q 1°T¼bÔA‰ˆˆaÜ�Š˜q 1™u q¨Q i°×1CÑ1CÄUÁWÁ_ÓUÐUr7   c           	     ó  € \         P                  ! V4      \         P                  ! \         P                  ! V) \         P                  ! V4      ,          4      ) 4      ,
          V^,           \         P                  ! V4      ,          ,
          # r_   )rQ   r  rf  rp  s   &&&&r5   rs  Útruncpareto_gen._logpdf_pos_b()  sM   € Ü�vŠv�a‹yœ2Ÿ6š6¤2§8¢8¨Q¨B¬r¯vªv°a«y­LÓ#9Ð"9Ó:Õ:¸aÀ½cÄ2Ç6Â6È!Ã9½_ÕLÐLr7   c                ó„   € \        WVR \        R7      w  rp^W) ,          ,
          ^^W2,          ,          ,
          ,          # rk  ro  rp  s   &&&&r5   ry   Útruncpareto_gen._cdf+)  s3   € Ü˜Q 1°T¼bÔA‰ˆˆaØ�A�r•E•	˜a ! A¥D¥&�jÕ)Ð)r7   c                ó�   <€ \        WVR \        R7      w  rp\        P                  ! V^ 8„  WV3V P                  \
        SV `  4      # rk  )r   rQ   r  r  Ú_logcdf_pos_br@   r  rt  s   &&&&€r5   r  Útruncpareto_gen._logcdf/)  rv  r7   c                óŽ   € \         P                  ! W) ,          ) 4      \         P                  ! RW2,          ,          4      ,
          # rÓ  r—  rp  s   &&&&r5   r|  Útruncpareto_gen._logcdf_pos_b3)  s+   € Ü�xŠx˜˜B�˜Ó¤"§(¢(¨2¨a­d­7Ó"3Õ3Ð3r7   c                ó˜   € \        WVR \        R7      w  rp\        ^^^W2,          ,          ,
          V,          ,
          RV,          4      # ©Trl  r  ©r   rQ   r¨  ©rD   rƒ   r™   r\  s   &&&&r5   r„   Útruncpareto_gen._ppf6)  s:   € Ü˜Q 1°T¼bÔA‰ˆˆaÜ�1˜˜A˜a�d�F�
 A•~Õ% r¨!¥tÓ,Ð,r7   c                óž   € \        WVR \        R7      w  rpW) ,          ^W2,          ,          ,
          ^^W2,          ,          ,
          ,          # rk  ro  rp  s   &&&&r5   r~   Útruncpareto_gen._sf:)  s9   € Ü˜Q 1°T¼bÔA‰ˆˆaØ�2•˜˜!�$�• 1 q¨­¥v¥:Õ.Ð.r7   c                ó�   <€ \        WVR \        R7      w  rp\        P                  ! V^ 8„  WV3V P                  \
        SV `  4      # rk  )r   rQ   r  r  Ú_logsf_pos_br@   r
  rt  s   &&&&€r5   r
  Útruncpareto_gen._logsf>)  s>   ø€ Ü˜Q 1°T¼bÔA‰ˆˆaÜ�Š˜q 1™u q¨Q i°×1BÑ1BÄEÁGÁNÓSÐSr7   c                ó´   € \         P                  ! W) ,          ^W2,          ,          ,
          4      \         P                  ! RW2,          ,          4      ,
          # rÓ  r…  rp  s   &&&&r5   rˆ  Útruncpareto_gen._logsf_pos_bB)  s3   € Ü�vŠv�a˜•e˜a ¥�f•nÓ%¬¯ª°°AµDµÓ(9Õ9Ð9r7   c                ó²   € \        WVR \        R7      w  rp\        ^W2,          ,          ^^W2,          ,          ,
          V,          ,           RV,          4      # r�  r‚  rƒ  s   &&&&r5   rˆ   Útruncpareto_gen._isfE)  s@   € Ü˜Q 1°T¼bÔA‰ˆˆaÜ�1�Q•T•6˜Q  1¥4¥�Z¨�NÕ*¨B¨q­DÓ1Ð1r7   c                óü   € \         P                  ! V^^W!,          ,          ,
          ,          4      V^,           \         P                  ! V4      W!,          ^,
          ,          ^V,          ,
          ,          ,           ) # r_   rc  rf  s   &&&r5   r  Útruncpareto_gen._entropyI)  sS   € Ü—’˜˜1˜q ¥�v�:�Ó'Ø�a•Cœ"Ÿ&š& ›) Q¥T¨A¥XÕ.°°1µÕ4Õ5õ6ð 7ð 	7r7   c                óH  € \        WVR \        R7      w  rpW8H  P                  4       '       d9   V\        P                  ! V4      ,          ^^W2,          ,          ,
          ,          # W"V,
          ,          W2,          W1,          ,
          ,          W2,          ^,
          ,          # rk  )r   rQ   r%  r  )rD   rc   r™   r\  s   &&&&r5   r,  Útruncpareto_gen._munpM)  sh   € Ü˜Q 1°T¼bÔA‰ˆˆaØ‰F�<‰<�>Š>Ø”R—V’V˜A“Y•; ! a¨­¥f¥*Õ-Ð-à˜!�•9 ¥ q¥t¥Õ,°µ°qµÕ9Ð9r7   c                ó¸   € \        V\        4      '       d   VP                  4       p\        P	                  V4      w  r#p\        V4      V,
          V,          pW%W43# rO   )r>   r)   rÕ  rÄ  rB   r.  )rD   rE   r™   r-   r.   r\  s   &&    r5   r×  Útruncpareto_gen._fitstartT)  sJ   € Ü�dœL×)Ò)Ø—>‘>Ó#ˆDÜŸ
™
 4Ó(‰ˆ�Ü�‹Y˜�_˜eÕ#ˆØ�SÐÐr7   c                ó&  <a aaa a!a"a#a$a%€ VP                  R R4      '       d   \        S&S `  ! S.VO5/ VB # R o#R o"VV"V#3R loV%3R lo V$V%3R lpV$3R lo!RVVV V!V"3R llpR	 pV&V 3R
 lp\        S SW#4      pVw  oršr¼SP	                  4       SP                  4       uo$o%\        P                  ! S$\        P                  ) 4      pV	e   V
e   Ve   Ve   \        R4      hV
Efý   VEfø   VEfó   V	Ef$   VV V!V"3R lp\        P                  ! S$\        P                  ) 4      pTp^ pV^,
          pV\        P                  ) 8”  dD   V! V4      V! V4      ,          ^ 8¼  d*   V^,          pV\        P                  ! RV4      ,
          pKY  V\        P                  ) 8”  g   V! S.VO5/ VB # \        VVV3R7      pVP                  '       g   V! S.VO5/ VB # VP                  R,
          pV^,
          p^ pV\        P                  ) 8”  dD   V! V4      V! V4      ,          ^ 8¼  d*   V^,          pV\        P                  ! RV4      ,
          pKY  V\        P                  ) 8”  g   V! S.VO5/ VB # \        VVV3R7      pVP                  '       g   V! S.VO5/ VB # VP                  pS!! V4      pS ! VV4      pS! VVV4      pSV,
          V,          p\	        ^S#! V4      ,          ^S"! V4      ^,
          ,          4      pVV8  g   V! S.VO5/ VB # EM>TpV^,
          p^ pV\        P                  ) 8”  d7   V! VV	4      V! Wù4      ,          ^ 8¼  d   V^,          pV^V,          ,
          pKL  V\        P                  ) 8”  g   V! S.VO5/ VB # \        WY3VV3R7      pVP                  '       g   V! S.VO5/ VB # VP                  pS!! V4      pS ! VV4      pT	pEMtVe   TMV! W¬4      pT;'       g	    S!! V4      pT
;'       g
    S ! VV4      pVe+   SP	                  4       V,
          ^ 8  d   \        R^VR7      hV
'       dD   Ve@   V'       d8   SP                  4       W¬,          V,           8”  d   \        R^S ! VV4      R7      hV	fÃ   SV,
          V,          pS#! V4      p\        P                  ! V4      p^V,          V8  g   V! S.VO5/ VB # ^V,          ^VV,
          ,          ,           p\        P                  ! ^V,          ^ 4      p \        VVV3VV3R7      pVP                  '       g   V! S.VO5/ VB # VP                  pMT	pVV,           S$8  gO   V'       d(   \        P                  ! V\        P                  ) 4      pMS!! V4      p\        P                  ! V^ 4      pVV,          V,           S%8”  g/   S ! VV4      p\        P                  ! V\        P                  4      p\        P                   ! S P#                  VV4      4      '       d   V^ 8”  g   V! S.VO5/ VB # VVVV3pVf>   Vf:   V! S.VO5/ VB pS P%                  VS4      pS P%                  VS4      pVV8  d   V# V#   \         d    Tp EL7i ; i)rE  Fc                 óV   € \         P                  ! \         P                  ! V 4      4      # rO   )rQ   r&  r  rÕ   s   &r5   Úlog_meanÚ%truncpareto_gen.fit.<locals>.log_meana)  s   € Ü—7’7œ2Ÿ6š6 !›9Ó%Ð%r7   c                 óJ   € ^\         P                  ! ^V ,          4      ,          # r_   )rQ   r&  rÕ   s   &r5   Ú	harm_meanÚ&truncpareto_gen.fit.<locals>.harm_meand)  s   € Ø”R—W’W˜Q˜q�S“\•>Ð!r7   c                 ó  <€ SV,
          V,          pS! V4      pS	! V4      pV^,
          V,          p^V^,
          V^^V ,          ,
          V,          \         P                  ! V 4      ,          ,
          ,          ,
          V,          # r_   rc  )
r\  r-   r.   rµ  Úharm_mÚlog_mÚquotrE   r™  r–  s
   &&&    €€€r5   Úget_bÚ"truncpareto_gen.fit.<locals>.get_bg)  si   ø€ Ø�c•˜5Õ ˆAÙ˜q“\ˆFÙ˜Q“KˆEØ˜1•H˜eÕ#ˆDØ˜˜a� D¨A°°!µ­G°VÕ+;¼B¿FºFÀ1»IÕ+EÕ$EÕFÕFÈÕMÐMr7   c                 ó$   <€ SV ,
          V,          # rO   r‹   )r-   r.   Úmxs   &&€r5   Úget_cÚ"truncpareto_gen.fit.<locals>.get_cn)  s   ø€ Ø˜•H˜eÕ#Ð#r7   c                 ó~   <€ V'       d   SV,
          pV# V '       d!   V S,          S,
          V ^,
          ,          pV# R# )rM   Nr‹   )rT  r  r-   rý	  r¢  s   && €€r5   Úget_locÚ$truncpareto_gen.fit.<locals>.get_locq)  s7   ø€ ßØ˜6•k�Ø�
ßØ˜"•u˜r•z B¨¥FÕ+�Ø�
ñ r7   c                 ó   <€ SV ,
          # rO   r‹   )r-   rý	  s   &€r5   r1  Ú&truncpareto_gen.fit.<locals>.get_scaley)  s   ø€ Ø˜•8ˆOr7   c                 ó  <€ S	! V 4      pS! W4      pVf
   S! W0V4      MTpS
! SV ,
          V,          4      p^^V^,
          W4^,           ,          V,
          ,          ,           ^^V^,           ,          ,
          ,          V,          ,
          # rO   r‹   )r-   r9  r.   r\  r™   rœ  rE   rŸ  r£  r1  r™  s   &&    €€€€€r5   rå
  Ú$truncpareto_gen.fit.<locals>.dL_dLoc)  sv   ø€ ñ ˜c“NˆEÙ�cÓ!ˆAØ(*ª
‘�a˜eÔ$¸ˆAÙ  s¥
¨EÕ1Ó2ˆFØ˜˜Q �U Q¨1­¥X°¥\Õ2Õ2°q¸1¸aÀ½c½7µ{ÕCÀfÕLÕLÐLr7   c                 ó~   € V \         P                  ! W,          ^W,          ,
          ,          4      V,          ,
          # r_   r—  )r™   ÚlogcÚlogms   &&&r5   ÚdL_dBÚ"truncpareto_gen.fit.<locals>.dL_dBˆ)  s*   € ð ”r—x’x ¥¨!¨a­f­*Õ 5Ó6¸Õ=Õ=Ð=r7   c                 ó4   <€ \         \        S`
  ! V .VO5/ VB # rO   )r@   rb  rB   )rE   rF   ÚkwargsrØ  rD   s   &*,€€r5   ÚfallbackÚ%truncpareto_gen.fit.<locals>.fallbackŽ)  s   ø€ äœ¨$Ò3°DÐJ¸4ÒJÀ6ÑJÐJr7   z2All parameters fixed.There is nothing to optimize.c                 óÐ   <€ S! V 4      pS! W4      pS! SV ,
          V,          4      p^^V^,
          ,          ,           \         P                  ! V4      ,          V,          ^,
          # r_   rc  )r-   r.   r\  rœ  rE   r£  r1  r™  s   &   €€€€r5   Úcond_bÚ#truncpareto_gen.fit.<locals>.cond_bŸ)  sR   ø€ á% c›N�EÙ˜cÓ)�AÙ&¨¨s­
°EÕ'9Ó:�FØ  1 Q¥3¥�K¬2¯6ª6°!«9Õ4°vÕ=ÀÕAÐAr7   rÒ   rÜ  gü©ñÒMbP?ÚtruncparetorÛ  rO   )r2   r@   rB   rR  rR  r.  rQ   rí
  rk   r"  rU  r*   rî
  rS  rƒ  r  r%  rd   rè
  )'rD   rE   rF   r4   r¦  rå
  r¯  r³  rï
  rã  rT  r  r  Úmn_infr¶  rT   rS  rS   r›  r-   r.   r\  r™   Ústd_dataÚ
up_bound_br®  r­  Úparams_overrideÚparams_superÚnllf_overrideÚ
nllf_superrŸ  r£  r1  r™  r–  rý	  r¢  rØ  s'   ff*,                           @@@@@@@€r5   rB   Útruncpareto_gen.fit[)  s8  ÿù€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ò	&ò	"÷	Nõ	$ö	õ	÷	Mó 	Mò	>ö	Kô 1°°t¸TÓHˆ
Ø%/Ñ"ˆˆb�dØ—‘“˜TŸX™X›ZˆˆˆBÜ—’˜b¤2§6¡6 'Ó*ˆàŠNØ’NØÒ$ØÒ&Üð =ó >ð >à‹Z˜D›L¨V«^Ø‹z÷Bð Bô Ÿš b¬2¯6©6¨'Ó2�Ø�Ø�Ø !��Ø¤"§&¡& Ô(Ù" 6›N©6°&«>Õ9¸QÔ>Ø˜•F�AØ#¤b§h¢h¨r°1£oÕ5’FØ¤§¡ Ô'Ù# DÐ8¨4Ò8°4Ñ8Ð8Ü! &°6¸6Ð2BÔC�Ø—}—}�}Ù# DÐ8¨4Ò8°4Ñ8Ð8ð Ÿ™ D��Ø !��Ø�Ø¤"§&¡& Ô(Ù# F›O©G°F«OÕ;¸qÔ@Ø˜•F�AØ#¤b§h¢h¨r°1£oÕ5’FØ¤§¡ Ô'Ù# DÐ8¨4Ò8°4Ñ8Ð8Ü! '°F¸FÐ3CÔD�Ø—}—}�}Ù# DÐ8¨4Ò8°4Ñ8Ð8Ø—h‘h�Ù! #›�Ù˜#˜uÓ%�Ù˜!˜S %Ó(�à  3�J¨Õ-�ä  ¡8¨HÓ#5Õ!5Ø!"¡I¨hÓ$7¸Õ$9Õ!:ó<�
à˜JœÙ# DÐ8¨4Ò8°4Ñ8Ð8ñ 'ð
  �Ø !��Ø�à¤§¡ Ô'Ù# F¨BÓ/Ù% fÓ1õ2Ø56ô7à˜•F�AØ# a¨¥d�]’FØ¤§¡ Ô'Ù# DÐ8¨4Ò8°4Ñ8Ð8Ü! '¨5Ø+1°6Ð*:ô<�à—}—}�}Ù# DÐ8¨4Ò8°4Ñ8Ð8Ø—h‘h�Ù! #›�Ù˜#˜uÓ%�Ø’ð Ò*‘$±¸Ó0CˆCØ×,Ð,™i¨›nˆEØ×'Ð'‘e˜C Ó'ˆAð Ò D§H¡H£J°Õ$5¸Ô$9Ü" =¸ÀÔCÐC÷ �tÒ'¯VØ—8‘8“: ¥	¨DÕ 0Ô0Ü& }¸AÙ-2°3¸Ó->ô@ð @ð ŠzØ  3�J¨Õ-�Ù Ó)�Ü—v’v˜a“y�à˜$� œÙ# DÐ8¨4Ò8°4Ñ8Ð8à˜4� ! T¨D¥[¥/Õ1�ÜŸš a¨¥f¨aÓ0�ðÜ% e¨d°D¨\Ø/5°vÐ.>ô@�Cð Ÿ=Ÿ=˜=Ù'¨Ð<¨tÒ<°tÑ<Ð<ØŸ™‘Að �ð �c•	˜RÔßÜ—l’l 3¬¯©¨Ó0‘á! #›�ÜŸš U¨AÓ.�Ø�%•˜•˜rÔ!Ù�c˜5Ó!ˆAÜ—’˜Q¤§¡Ó'ˆAä—’�t—~‘~ a¨Ó+×,Ò,°%¸!´)Ù˜DÐ0 4Ò0¨4Ñ0Ð0à˜Q  UÐ*ˆØŠ<˜FšNñ
 $ DÐ8¨4Ò8°4Ñ8ˆLØ ŸI™I o°tÓ<ˆMØŸ™ <°Ó6ˆJØ˜MÔ)Ø#Ð#àÐøôE "ô Ø“Aðús   Ô/Y? Õ	Y? Ù?ZÚZr‹   )rŒ   r�   rŽ   r�   r�   rm   rd   r¥   ru   rý   rs  ry   r  r|  r„   r~   r
  rˆ  rˆ   r  r,  r×  rK   r   r   rB   r‘   r’   r  r   s   @@r5   rb  rb  Û(  s�   ù‡ € ñ6òpò
$òò,õ
VòMò*õVò4ò-ò/õTò:ò2ò7ò:ò ð Ù˜MÓ*ôZó +ó ÷Zð Zr7   rb  r¸  c                   ól   a € ] tR tRt o Rt]P                  tR tR t	R t
R tR tR tR	 tR
 tRtV tR# )Útukeylambda_geni>*  aò  A Tukey-Lamdba continuous random variable.

%(before_notes)s

Notes
-----
A flexible distribution, able to represent and interpolate between the
following distributions:

- Cauchy                (:math:`lambda = -1`)
- logistic              (:math:`lambda = 0`)
- approx Normal         (:math:`lambda = 0.14`)
- uniform from -1 to 1  (:math:`lambda = 1`)

`tukeylambda` takes a real number :math:`lambda` (denoted ``lam``
in the implementation) as a shape parameter.

%(after_notes)s

%(example)s

c                ó.   € \         P                  ! V4      # rO   rÅ  ©rD   Úlams   &&r5   rd   Útukeylambda_gen._argcheckW*  s   € Ü�{Š{˜3ÓÐr7   c                ó^   € \        R R\        P                  ) \        P                  3R4      .# )rÅ  Fr4  rj   rl   s   &r5   rm   Útukeylambda_gen._shape_infoZ*  s%   € Ü˜5 %¬2¯6©6¨'´2·6±6Ð):¸NÓKÐLÐLr7   c                ód   € \         P                  ! V^ 8„  VR \        P                  R7      pV) V3# )r   c                 ó   € ^V ,          # r_   r‹   )rÅ  s   &r5   r  Ú.tukeylambda_gen._get_support.<locals>.<lambda>_*  s   € ¨¨#®r7   r  rU  )rD   rÅ  r™   s   && r5   r¥   Útukeylambda_gen._get_support]*  s/   € Ü�OŠO˜C !™G SÙ-Ü')§v¡vô/ˆð ˆr�1ˆuˆr7   c           
     ó  € \         P                  ! \        P                  ! W4      4      pW2R ,
          ,          \         P                  ! ^V,
          4      VR ,
          ,          ,           p\         P                  ! RR7      ;_uu_ 4        R \         P                  ! V4      ,          p\         P
                  ! V^ 8*  \        V4      R \         P                  ! V4      ,          8  ,          VR4      uuRRR4       #   + '       g   i     R# ; i)r–   rl  rm  r•   N)rQ   r#  r|   Útklmbdaro  r±  r	  )rD   rt   rÅ  ÚFxr  s   &&&  r5   ru   Útukeylambda_gen._pdfc*  sž   € Ü�ZŠZœŸ
š
 1Ó*Ó+ˆØ�c•'�]œbŸjšj¨¨2­Ó.°#°cµ'Õ:Õ:ˆÜ�[Š[ ×)Ö)Ø”R—Z’Z “^Õ#ˆBÜ—8’8˜S A™X¬#¨a«&°3´r·z²zÀ#³Õ3FÑ*FÕGÈÈSÓQ÷ *×)×)Ó)ús   Â	A&C:Ã:D	c                ó.   € \         P                  ! W4      # rO   )r|   rÎ  )rD   rt   rÅ  s   &&&r5   ry   Útukeylambda_gen._cdfj*  s   € Ü�zŠz˜!Ó!Ð!r7   c                óh   € \         P                  ! W4      \         P                  ! V) V4      ,
          # rO   )r|   rå  râ  )rD   rƒ   rÅ  s   &&&r5   r„   Útukeylambda_gen._ppfm*  s#   € Ü�yŠy˜Ó ¤2§;¢;°¨r°3Ó#7Õ7Ð7r7   c                ó2   € ^ \        V4      ^ \        V4      3# r  )Ú_tlvarÚ_tlkurtrÄ  s   &&r5   r   Útukeylambda_gen._statsp*  s   € Ø”&˜“+˜q¤'¨#£,Ð.Ð.r7   c                óN   a€ V3R  lp\         P                  ! V^ ^4      ^ ,          # )c                 ó�   <€ \         P                  ! \        V S^,
          4      \        ^V ,
          S^,
          4      ,           4      # r_   )rQ   r  r¨  )rH  rÅ  s   &€r5   ÚintegÚ'tukeylambda_gen._entropy.<locals>.integt*  s/   ø€ Ü—6’6œ#˜a  Q¥›-¬¨A¨a­C°°Qµ«Õ7Ó8Ð8r7   )r   r,  )rD   rÅ  rÛ  s   &f r5   r  Útukeylambda_gen._entropys*  s    ø€ õ	9ä�~Š~˜e Q¨Ó*¨1Õ-Ð-r7   r‹   N)rŒ   r�   rŽ   r�   r�   r   rI  rJ  rd   rm   r¥   ru   ry   r„   r   r  r‘   r’   r“   s   @r5   rÂ  rÂ  >*  sF   ø‡ € ñð, "×4Ñ4€Mò òMòòRò"ò8ò/÷.ð .r7   rÂ  Útukeylambdac                   ó&   a € ] tR tRt o R tRtV tR# )ÚFitUniformFixedScaleDataErrori|*  c                ó"   € R V RV R2V n         R# )z Invalid values in `data`.  Maximum likelihood estimation with the uniform distribution and fixed scale requires that np.ptp(data) <= fscale, but np.ptp(data) = z and fscale = r1   Nr…  )rD   rG  r  s   &&&r5   rˆ  Ú&FitUniformFixedScaleDataError.__init__}*  s$   € ð:à:=¸ð ?Ø�x˜qð"ð 	Ž	r7   r…  N)rŒ   r�   rŽ   r�   rˆ  r‘   r’   r“   s   @r5   rà  rà  |*  s   ø‡ € ÷
ð 
r7   rà  c                   ób   a € ] tR tRt o RtR tRR ltR tR tR t	R	 t
R
 t]R 4       tRtV tR# )Úuniform_geni†*  zôA uniform continuous random variable.

In the standard form, the distribution is uniform on ``[0, 1]``. Using
the parameters ``loc`` and ``scale``, one obtains the uniform distribution
on ``[loc, loc + scale]``.

%(before_notes)s

%(example)s

c                ó   € . # rO   r‹   rl   s   &r5   rm   Úuniform_gen._shape_info’*  r¼   r7   Nc                ó(   € VP                  R RV4      # rr  )r´  ró   s   &&&r5   rö   Úuniform_gen._rvs•*  s   € Ø×#Ñ# C¨¨dÓ3Ð3r7   c                ó   € R W8H  ,          # r8  r‹   r¿   s   &&r5   ru   Úuniform_gen._pdf˜*  s   € Ø�A‘F�|Ðr7   c                ó   € V# rO   r‹   r¿   s   &&r5   ry   Úuniform_gen._cdf›*  ó   € Øˆr7   c                ó   € V# rO   r‹   rÉ   s   &&r5   r„   Úuniform_gen._ppfž*  rí  r7   c                ó   € R# )r£   )r£   gUUUUUUµ?r   g333333ó¿r‹   rl   s   &r5   r   Úuniform_gen._stats¡*  s   € Ø#Ð#r7   c                ó   € R # r[  r‹   rl   s   &r5   r  Úuniform_gen._entropy¤*  rN  r7   c                óþ  € \        V4      ^ 8”  d   \        R4      hVP                  RR4      pVP                  RR4      p\        V4       Ve   Ve   \	        R4      h\
        P                  ! V4      p\
        P                  ! V4      P                  4       '       g   \	        R4      hVfo   Vf(   VP                  4       p\
        P                  ! V4      pM‘TpVP                  4       V,
          pVP                  4       V8  d   \        RWfV,           R7      hMN\
        P                  ! V4      pW…8”  d   \        W…R	7      hVP                  4       R
WX,
          ,          ,
          pTp\        V4      \        V4      3# )aÎ  
Maximum likelihood estimate for the location and scale parameters.

`uniform.fit` uses only the following parameters.  Because exact
formulas are used, the parameters related to optimization that are
available in the `fit` method of other distributions are ignored
here.  The only positional argument accepted is `data`.

Parameters
----------
data : array_like
    Data to use in calculating the maximum likelihood estimate.
floc : float, optional
    Hold the location parameter fixed to the specified value.
fscale : float, optional
    Hold the scale parameter fixed to the specified value.

Returns
-------
loc, scale : float
    Maximum likelihood estimates for the location and scale.

Notes
-----
An error is raised if `floc` is given and any values in `data` are
less than `floc`, or if `fscale` is given and `fscale` is less
than ``data.max() - data.min()``.  An error is also raised if both
`floc` and `fscale` are given.

Examples
--------
>>> import numpy as np
>>> from scipy.stats import uniform

We'll fit the uniform distribution to `x`:

>>> x = np.array([2, 2.5, 3.1, 9.5, 13.0])

For a uniform distribution MLE, the location is the minimum of the
data, and the scale is the maximum minus the minimum.

>>> loc, scale = uniform.fit(x)
>>> loc
2.0
>>> scale
11.0

If we know the data comes from a uniform distribution where the support
starts at 0, we can use ``floc=0``:

>>> loc, scale = uniform.fit(x, floc=0)
>>> loc
0.0
>>> scale
13.0

Alternatively, if we know the length of the support is 12, we can use
``fscale=12``:

>>> loc, scale = uniform.fit(x, fscale=12)
>>> loc
1.5
>>> scale
12.0

In that last example, the support interval is [1.5, 13.5].  This
solution is not unique.  For example, the distribution with ``loc=2``
and ``scale=12`` has the same likelihood as the one above.  When
`fscale` is given and it is larger than ``data.max() - data.min()``,
the parameters returned by the `fit` method center the support over
the interval ``[data.min(), data.max()]``.

rP  r  Nr  r   r!  r´  rÛ  )rG  r  r£   )rç  r3   r2   r6   r"  rQ   r#  r$  r%  rR  rG  r.  rƒ  rà  r  )	rD   rE   rF   r4   r  r  r-   r.   rG  s	   &&*,     r5   rB   Úuniform_gen.fit§*  sF  € ôV ˆt‹9�qŒ=ÜÐ1Ó2Ð2à�x‰x˜ Ó%ˆØ—‘˜( DÓ)ˆä$ TÔ*àÒ Ò 2äð )ó *ð *ô �zŠz˜$Óˆä�{Š{˜4Ó ×$Ñ$×&Ò&ÜÐCÓDÐDð> Š>àŠ|à—h‘h“j�ÜŸš˜t›‘ð �ØŸ™›
 SÕ(�Ø—8‘8“: Ô#Ü& y¸ÈÅ;ÔOÐOð $ô —&’&˜“,ˆCØŒ|Ü3¸ÔKÐKð —(‘(“*˜s F¥LÕ1Õ1ˆCØˆEô �S‹zœ5 ›<Ð'Ð'r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rö   ru   ry   r„   r   r  rK   rB   r‘   r’   r“   s   @r5   rä  rä  †*  sC   ø‡ € ñ
òô4òòòò$òð ñR(ó öR(r7   rä  r´  c                   óÚ   a a€ ] tR tRt oRtR tR tRR lt]! ]	4      V 3R l4       t
R tR tR	 tR
 tR t]! ]	RR7      RV 3R ll4       t]]! ]	RR7      V 3R l4       4       tRtVtV ;t# )Úvonmises_geni@+  aE  A Von Mises continuous random variable.

%(before_notes)s

See Also
--------
scipy.stats.vonmises_fisher : Von-Mises Fisher distribution on a
                              hypersphere

Notes
-----
The probability density function for `vonmises` and `vonmises_line` is:

.. math::

    f(x, \kappa) = \frac{ \exp(\kappa \cos(x)) }{ 2 \pi I_0(\kappa) }

for :math:`-\pi \le x \le \pi`, :math:`\kappa \ge 0`. :math:`I_0` is the
modified Bessel function of order zero (`scipy.special.i0`).

`vonmises` is a circular distribution which does not restrict the
distribution to a fixed interval. Currently, there is no circular
distribution framework in SciPy. The ``cdf`` is implemented such that
``cdf(x + 2*np.pi) == cdf(x) + 1``.

`vonmises_line` is the same distribution, defined on :math:`[-\pi, \pi]`
on the real line. This is a regular (i.e. non-circular) distribution.

Note about distribution parameters: `vonmises` and `vonmises_line` take
``kappa`` as a shape parameter (concentration) and ``loc`` as the location
(circular mean). A ``scale`` parameter is accepted but does not have any
effect.

Examples
--------
Import the necessary modules.

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.stats import vonmises

Define distribution parameters.

>>> loc = 0.5 * np.pi  # circular mean
>>> kappa = 1  # concentration

Compute the probability density at ``x=0`` via the ``pdf`` method.

>>> vonmises.pdf(0, loc=loc, kappa=kappa)
0.12570826359722018

Verify that the percentile function ``ppf`` inverts the cumulative
distribution function ``cdf`` up to floating point accuracy.

>>> x = 1
>>> cdf_value = vonmises.cdf(x, loc=loc, kappa=kappa)
>>> ppf_value = vonmises.ppf(cdf_value, loc=loc, kappa=kappa)
>>> x, cdf_value, ppf_value
(1, 0.31489339900904967, 1.0000000000000004)

Draw 1000 random variates by calling the ``rvs`` method.

>>> sample_size = 1000
>>> sample = vonmises(loc=loc, kappa=kappa).rvs(sample_size)

Plot the von Mises density on a Cartesian and polar grid to emphasize
that it is a circular distribution.

>>> fig = plt.figure(figsize=(12, 6))
>>> left = plt.subplot(121)
>>> right = plt.subplot(122, projection='polar')
>>> x = np.linspace(-np.pi, np.pi, 500)
>>> vonmises_pdf = vonmises.pdf(x, loc=loc, kappa=kappa)
>>> ticks = [0, 0.15, 0.3]

The left image contains the Cartesian plot.

>>> left.plot(x, vonmises_pdf)
>>> left.set_yticks(ticks)
>>> number_of_bins = int(np.sqrt(sample_size))
>>> left.hist(sample, density=True, bins=number_of_bins)
>>> left.set_title("Cartesian plot")
>>> left.set_xlim(-np.pi, np.pi)
>>> left.grid(True)

The right image contains the polar plot.

>>> right.plot(x, vonmises_pdf, label="PDF")
>>> right.set_yticks(ticks)
>>> right.hist(sample, density=True, bins=number_of_bins,
...            label="Histogram")
>>> right.set_title("Polar plot")
>>> right.legend(bbox_to_anchor=(0.15, 1.06))

c                ó@   € \        R R^ \        P                  3R4      .# )rè	  Fri   rj   rl   s   &r5   rm   Úvonmises_gen._shape_info +  s   € Ü˜7 E¨A¬r¯v©v¨;¸ÓFÐGÐGr7   c                ó   € V^ 8¬  # r  r‹   r 
  s   &&r5   rd   Úvonmises_gen._argcheck£+  s   € Ø˜‰zÐr7   c                ó(   € VP                  R WR7      # )r•   r³  )Úvonmises)rD   rè	  rô   rõ   s   &&&&r5   rö   Úvonmises_gen._rvs¦+  s   € Ø×$Ñ$ S¨%Ð$Ó;Ð;r7   c                óÐ   <€ \         SV `  ! V/ VB p\        P                  ! V\        P                  ,           ^\        P                  ,          4      \        P                  ,
          # rD  ©r@   r)  rQ   Úmodr  ©rD   rF   r4   r)  rØ  s   &*, €r5   r)  Úvonmises_gen.rvs©+  s@   ø€ ä‰gŠk˜4Ð( 4Ñ(ˆÜ�vŠv�cœBŸE™E•k 1¤R§U¡U¥7Ó+¬b¯e©eÕ3Ð3r7   c                óÒ   € \         P                  ! V\        P                  ! V4      ,          4      ^\         P                  ,          \        P
                  ! V4      ,          ,          # rD  )rQ   rÓ   r|   Úcosm1r  ræ  rë	  s   &&&r5   ru   Úvonmises_gen._pdf®+  s:   € ô
 �vŠv�eœBŸHšH Q›KÕ'Ó(¨A¬b¯e©e­G´B·F²F¸5³MÕ,AÕBÐBr7   c                óú   € V\         P                  ! V4      ,          \        P                  ! ^\        P                  ,          4      ,
          \        P                  ! \         P
                  ! V4      4      ,
          # rD  )r|   r  rQ   r  r  ræ  rë	  s   &&&r5   rý   Úvonmises_gen._logpdfµ+  s@   € à”r—x’x “{Õ"¤R§V¢V¨A¬b¯e©e­G£_Õ4´r·v²v¼b¿fºfÀU»mÓ7LÕLÐLr7   c                ó.   € \         P                  ! W!4      # rO   )r   Úvon_mises_cdfrë	  s   &&&r5   ry   Úvonmises_gen._cdf¹+  s   € Ü×#Ò# EÓ-Ð-r7   c                ó   € R# r*  r‹   r 
  s   &&r5   Ú_stats_skipÚvonmises_gen._stats_skip¼+  r,  r7   c                ó  € V) \         P                  ! V4      ,          \         P                  ! V4      ,          \        P                  ! ^\        P
                  ,          \         P                  ! V4      ,          4      ,           V,           # rD  )r|   Úi1eræ  rQ   r  r  r 
  s   &&r5   r  Úvonmises_gen._entropy¿+  sV   € ð �œŸš ›Õ&¬¯ª°«Õ6Ü—’�qœ2Ÿ5™5•y¤2§6¢6¨%£=Õ0Ó1õ2Ø49õ:ð 	;r7   z¢        The default limits of integration are endpoints of the interval
        of width ``2*pi`` centered at `loc` (e.g. ``[-pi, pi]`` when
        ``loc=0``).

r  c           	     óœ   <€ \         P                  ) \         P                  r©Vf	   W9,           pVf	   W:,           p\        SV `  ! WVWEWg3/ VB # rO   )rQ   r  r@   Úexpect)rD   r˜  rF   r-   r.   ÚlbÚubÚconditionalr4   r   r  rØ  s   &&&&&&&&,  €r5   r  Úvonmises_gen.expectË+  sS   ø€ ô —%‘%�œŸ™ˆBàŠ:Ø•ˆBØŠ:Ø•ˆBä‰wŠ~˜d¨#Ø#¨ñBØ<@ñBð 	Br7   a          Fit data is assumed to represent angles and will be wrapped onto the
        unit circle. `f0` and `fscale` are ignored; the returned shape is
        always the maximum likelihood estimate and the scale is always
        1. Initial guesses are ignored.

c                ó2  <€ VP                  R R4      '       d   \        SV `  ! V.VO5/ VB # \        WW#4      w  rrVV P                  \
        P                  ) 8X  d   \        SV `  ! V.VO5/ VB # \
        P                  ! V^\
        P                  ,          4      pR pR pVe   TMV! V4      p	Ve   TMV! W4      p
\
        P                  ! V	\
        P                  ,           ^\
        P                  ,          4      \
        P                  ,
          p	W©^3# )rE  Fc                 ó.   € \         P                  ! V 4      # rO   )rF  Úcircmean)rE   s   &r5   Úfind_muÚ!vonmises_gen.fit.<locals>.find_muî+  s   € Ü—>’> $Ó'Ð'r7   c                 ó¸  a€ \         P                  ! \         P                  ! W,
          4      4      \        V 4      ,          oS^8X  d   R# S^ 8”  dg   V3R lpS^S,
          ,          ^S,           ,          p^V,          pV! V4      ^ 8¼  d   V# V! V4      ^ 8:  d   V# \	        VRW43R7      pVP
                  # \         P                  ! \        4      P                  # )rM   g €à7yÃACc                 ót   <€ \         P                  ! V 4      \         P                  ! V 4      ,          S,
          # rO   )r|   r  ræ  )rè	  rI  s   &€r5   Úsolve_for_kappaÚ=vonmises_gen.fit.<locals>.find_kappa.<locals>.solve_for_kappa,  s#   ø€ ÜŸ6š6 %›=¬¯ª°«Õ6¸Õ:Ð:r7   r©  )r0   rQ  )	rQ   rè  rQ  rç  r*   rS  rÞ  r  rß  )rE   r-   r  Úlower_boundÚupper_boundÚroot_resrI  s   &&    @r5   Ú
find_kappaÚ$vonmises_gen.fit.<locals>.find_kappañ+  s¾   ø€ ô —’”r—v’v˜c�jÓ)Ó*¬3¨t«9Õ4ˆAð �AŒvñ Ø�Q”õ;ð    1¥�g q¨¥s�m�Ø �m�ñ # ;Ó/°1Ô4Ø&Ð&Ù$ [Ó1°QÔ6Ø&Ð&ä*¨?À8Ø4?Ð3Mô O�Hà#Ÿ=™=Ð(ô —x’x¤“×+Ñ+Ð+r7   )r2   r@   rB   rR  r˜   rQ   r  r  )rD   rE   rF   r4   rß
  r  r  r  r$  r-   rG  rØ  s   &&*,       €r5   rB   Úvonmises_gen.fitÛ+  sê   ø€ ð �8‰8�J ×&Ò&Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ä%@ÀØAEó&MÑ"ˆ�dà�6‰6”b—e‘e�VÔä‘7’;˜tÐ3 dÒ3¨dÑ3Ð3ô �vŠv�d˜A¤§¡�IÓ&ˆò	(ò6	,ðr Ò&‰d©G°D«Mˆà Ò,‘±*¸TÓ2Gˆä�fŠf�Sœ2Ÿ5™5•[ !¤b§e¡e¥)Ó,¬r¯u©uÕ4ˆØ˜1ˆ}Ðr7   r‹   r.  )Nr‹   r   rM   NNF)rŒ   r�   rŽ   r�   r�   rm   rd   rö   r   r   r)  ru   rý   ry   r  r  r	   r  rK   rB   r‘   r’   r  r   s   @@r5   r÷  r÷  @+  s¢   ù‡ € ñ^ò~Hòô<ñ ˜MÓ*ô4ó +ð4òCòMò.ò ò
;ñ ˜}ð 5ô ö
Bó	ð
Bð Ù˜}ð 5/ô 0ô
Nó0ó ÷Nð Nr7   r÷  rý  Úvonmises_linec                   óˆ   a € ] tR tRt o Rt]P                  tR tRR lt	R t
R tR tR	 tR
 tR tR tR tR tR tRtV tR# )r¥  i6,  a,  A Wald continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `wald` is:

.. math::

    f(x) = \frac{1}{\sqrt{2\pi x^3}} \exp(- \frac{ (x-1)^2 }{ 2x })

for :math:`x >= 0`.

`wald` is a special case of `invgauss` with ``mu=1``.

%(after_notes)s

%(example)s
c                ó   € . # rO   r‹   rl   s   &r5   rm   Úwald_gen._shape_infoM,  r¼   r7   Nc                ó*   € VP                  R R VR7      # r‚  rƒ  ró   s   &&&r5   rö   Úwald_gen._rvsP,  s   € Ø× Ñ   c°Ð Ó5Ð5r7   c                ó.   € \         P                  VR 4      # r8  )r¤  ru   r¿   s   &&r5   ru   Úwald_gen._pdfS,  s   € ä�}‰}˜Q Ó$Ð$r7   c                ó.   € \         P                  VR 4      # r8  )r¤  ry   r¿   s   &&r5   ry   Úwald_gen._cdfW,  ó   € Ü�}‰}˜Q Ó$Ð$r7   c                ó.   € \         P                  VR 4      # r8  )r¤  r~   r¿   s   &&r5   r~   Úwald_gen._sfZ,  s   € Ü�|‰|˜A˜sÓ#Ð#r7   c                ó.   € \         P                  VR 4      # r8  )r¤  r„   r¿   s   &&r5   r„   Úwald_gen._ppf],  r1  r7   c                ó.   € \         P                  VR 4      # r8  )r¤  rˆ   r¿   s   &&r5   rˆ   Úwald_gen._isf`,  r1  r7   c                ó.   € \         P                  VR 4      # r8  )r¤  rý   r¿   s   &&r5   rý   Úwald_gen._logpdfc,  ó   € Ü×Ñ  3Ó'Ð'r7   c                ó.   € \         P                  VR 4      # r8  )r¤  r  r¿   s   &&r5   r  Úwald_gen._logcdff,  r:  r7   c                ó.   € \         P                  VR 4      # r8  )r¤  r
  r¿   s   &&r5   r
  Úwald_gen._logsfi,  s   € Ü�‰˜q #Ó&Ð&r7   c                ó   € R# )r–   )r–   r–   r£  r·  r‹   rl   s   &r5   r   Úwald_gen._statsl,  s   € Ø"Ð"r7   c                ó,   € \         P                  R 4      # r8  )r¤  r  rl   s   &r5   r  Úwald_gen._entropyo,  s   € Ü× Ñ  Ó%Ð%r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   r   rI  rJ  rm   rö   ru   ry   r~   r„   rˆ   rý   r  r
  r   r  r‘   r’   r“   s   @r5   r¥  r¥  6,  sX   ø‡ € ñð( "×4Ñ4€Mòô6ò%ò%ò$ò%ò%ò(ò(ò'ò#÷&ð &r7   r¥  r„  c                   óv   a a€ ] tR tRt oRtR tR tR tR tR t	R t
R	 t]! ]4      V 3R
 l4       tRtVtV ;t# )Úwrapcauchy_geniv,  aS  A wrapped Cauchy continuous random variable.

%(before_notes)s

Notes
-----
The probability density function for `wrapcauchy` is:

.. math::

    f(x, c) = \frac{1-c^2}{2\pi (1+c^2 - 2c \cos(x))}

for :math:`0 \le x \le 2\pi`, :math:`0 < c < 1`.

`wrapcauchy` takes ``c`` as a shape parameter for :math:`c`.

%(after_notes)s

%(example)s

c                ó    € V^ 8„  V^8  ,          # r  r‹   r÷  s   &&r5   rd   Úwrapcauchy_gen._argcheckŒ,  s   € Ø�A‘˜!˜a™%Õ Ð r7   c                ó    € \        R RRR4      .# )r\  F)r   rM   r4  rO  rl   s   &r5   rm   Úwrapcauchy_gen._shape_info�,  s   € Ü˜3  v¨~Ó>Ð?Ð?r7   c                óÒ   € R W",          ,
          ^\         P                  ,          ^W",          ,           ^V,          \         P                  ! V4      ,          ,
          ,          ,          # r8  r’  r`  s   &&&r5   ru   Úwrapcauchy_gen._pdf’,  s;   € à�A•C•˜!œBŸE™E�' 1 Q¥S¥5¨¨1­¬R¯VªV°A«Y­Õ#6Õ7Õ8Ð8r7   c                ó�   € R  pR p^V,           ^V,
          ,          p\         P                  ! V\        P                  8  W3W44      # )c                 óª   € ^\         P                  ,          \         P                  ! V\         P                  ! V ^,          4      ,          4      ,          # r_   ©rQ   r  rÜ  rÉ  ©rt   Úcrs   &&r5   râ  Úwrapcauchy_gen._cdf.<locals>.f1˜,  s.   € à”R—U‘U•7œRŸYšY r¬"¯&ª&°°1µ«+¥~Ó6Õ6Ð6r7   c           	      óð   € ^^\         P                  ,          \         P                  ! V\         P                  ! ^\         P                  ,          V ,
          ^,          4      ,          4      ,          ,
          # r_   rM  rN  s   &&r5   ri  Úwrapcauchy_gen._cdf.<locals>.f2œ,  sA   € à�qœŸ™•w¤§¢¨2¬b¯fªf°a¼¿¹µgÀµkÀ1µ_Ó.EÕ+EÓ!FÕFÕFÐFr7   )r  r  rQ   r  )rD   rt   r\  râ  ri  rO  s   &&&   r5   ry   Úwrapcauchy_gen._cdf–,  s=   € ò	7ò	Gð �!�e�a˜!•e�_ˆÜ�Š˜q¤2§5¡5™y¨1¨'°2Ó:Ð:r7   c           
     óÞ  € R V,
          R V,           ,          p^\         P                  ! V\         P                  ! \         P                  V,          4      ,          4      ,          p^\         P                  ,          ^\         P                  ! V\         P                  ! \         P                  ^V,
          ,          4      ,          4      ,          ,
          p\         P                  ! VR8  WE4      # r‘  )rQ   rÜ  rÉ  r  r±  )rD   rƒ   r\  r˜  ÚrcqÚrcmqs   &&&   r5   r„   Úwrapcauchy_gen._ppf£,  sŠ   € Ø�1�u�s˜1•u�oˆØ”—	’	˜#œbŸfšf¤R§U¡U¨1¥W›oÕ-Ó.Õ.ˆØ”—‘�w�qœŸš 3¤r§v¢v¬b¯e©e°Q°qµS­kÓ':Õ#:Ó;Õ;Õ;ˆÜ�xŠx˜˜E™	 3Ó-Ð-r7   c                ó€   € \         P                  ! ^\         P                  ,          ^W,          ,
          ,          4      # rD  r  r÷  s   &&r5   r  Úwrapcauchy_gen._entropy©,  s#   € Ü�vŠv�aœŸ™•g˜q ¥�u•oÓ&Ð&r7   c                óà   € \        V\        4      '       d   VP                  4       pR \        P                  ! V4      \        P
                  ! V4      ^\        P                  ,          ,          3# r  )r>   r)   rÕ  rQ   rR  rG  r  )rD   rE   s   &&r5   r×  Úwrapcauchy_gen._fitstart¬,  sG   € ô �dœL×)Ò)Ø—>‘>Ó#ˆDØ”B—F’F˜4“L¤"§&¢&¨£,°´"·%±%µÕ"8Ð8Ð8r7   c                ó|   <€ \         SV `  ! V/ VB p\        P                  ! V^\        P                  ,          4      # rD  r   r  s   &*, €r5   r)  Úwrapcauchy_gen.rvs´,  s/   ø€ ä‰gŠk˜4Ð( 4Ñ(ˆÜ�vŠv�c˜1œRŸU™U�7Ó#Ð#r7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   ru   ry   r„   r  r×  r   r   r)  r‘   r’   r  r   s   @@r5   rD  rD  v,  sL   ù‡ € ñò*!ò@ò9ò;ò.ò'ò9ñ ˜MÓ*ô$ó +÷$ð $r7   rD  Ú
wrapcauchyc                   ój   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tRR ltRtV tR# )Úgennorm_geni¼,  aÀ  A generalized normal continuous random variable.

%(before_notes)s

See Also
--------
laplace : Laplace distribution
norm : normal distribution

Notes
-----
The probability density function for `gennorm` is [1]_:

.. math::

    f(x, \beta) = \frac{\beta}{2 \Gamma(1/\beta)} \exp(-|x|^\beta),

where :math:`x` is a real number, :math:`\beta > 0` and
:math:`\Gamma` is the gamma function (`scipy.special.gamma`).

`gennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
For :math:`\beta = 1`, it is identical to a Laplace distribution.
For :math:`\beta = 2`, it is identical to a normal distribution
(with ``scale=1/sqrt(2)``).

References
----------

.. [1] "Generalized normal distribution, Version 1",
       https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

.. [2] Nardon, Martina, and Paolo Pianca. "Simulation techniques for
       generalized Gaussian densities." Journal of Statistical
       Computation and Simulation 79.11 (2009): 1317-1329

.. [3] Wicklin, Rick. "Simulate data from a generalized Gaussian
       distribution" in The DO Loop blog, September 21, 2016,
       https://blogs.sas.com/content/iml/2016/09/21/simulate-generalized-gaussian-sas.html

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# ©r©  Fr4  rj   rl   s   &r5   rm   Úgennorm_gen._shape_infoç,  ó   € Ü˜6 5¨1¬b¯f©f¨+°~ÓFÐGÐGr7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  ©rD   rt   r©  s   &&&r5   ru   Úgennorm_gen._pdfê,  s   € Ü�vŠv�d—l‘l 1Ó+Ó,Ð,r7   c                ó®   € \         P                  ! R V,          4      \        P                  ! RV,          4      ,
          \	        V4      V,          ,
          # r¢   )rQ   r  r|   r  r	  rf  s   &&&r5   rý   Úgennorm_gen._logpdfí,  s4   € Ü�vŠv�c˜$•hÓ¤"§*¢*¨S°­XÓ"6Õ6¼¸Q»À½ÕEÐEr7   c                óÂ   € R \         P                  ! V4      ,          pR V,           V\        P                  ! RV,          \	        V4      V,          4      ,          ,
          # r¢   )rQ   rR   r|   rF  r	  ©rD   rt   r©  r\  s   &&& r5   ry   Úgennorm_gen._cdfð,  s?   € Ø”"—'’'˜!“*Õˆà�a•˜1œrŸ|š|¨C°­H´c¸!³f¸dµlÓCÕCÕCÐCr7   c                óÚ   € \         P                  ! VR ,
          4      pV\        P                  ! RV,          RV,           RV,          V,          ,
          4      RV,          ,          ,          # )r£   r–   rÒ   )rQ   rR   r|   rP  rk  s   &&& r5   r„   Úgennorm_gen._ppfõ,  sH   € Ü�GŠG�A˜•GÓˆà”2—?’? 3 t¥8¨c°A­g¸¸Q½¸q½Õ-@ÓAÀCÈÅHÕMÕMÐMr7   c                ó(   € V P                  V) V4      # rO   r×	  rf  s   &&&r5   r~   Úgennorm_gen._sfú,  s   € Ø�y‰y˜!˜˜TÓ"Ð"r7   c                ó&   € V P                  W4      ) # rO   r´  rf  s   &&&r5   rˆ   Úgennorm_gen._isfý,  s   € Ø—	‘	˜!Ó"Ð"Ð"r7   c                óÊ   € V^ 8X  d   R# V^,          ^ 8X  dL   \         P                  ! RV,          VR,           V,          .4      w  r4\        P                  ! WC,
          4      # R# )r   r–   r•   ©r|   r  rQ   rÓ   )rD   rc   r©  Úc1Úcns   &&&  r5   r,  Úgennorm_gen._munp -  sK   € Ø�Œ6ÙØˆq�5�AŒ:Ü—Z’Z  T¥¨A°­G°T­>Ð :Ó;‰FˆBÜ—6’6˜"�'“?Ð"ár7   c                ó  € \         P                  ! R V,          RV,          RV,          .4      w  r#pR\        P                  ! W2,
          4      R\        P                  ! WB,           RV,          ,
          4      R,
          3# )r–   r£  r§  r•   rÒ   rt  )rD   r©  ru  Úc3Úc5s   &&   r5   r   Úgennorm_gen._stats	-  sY   € Ü—Z’Z  T¥¨3¨t­8°S¸µXÐ >Ó?‰
ˆ�Ø”2—6’6˜"�'“? B¬¯ª¨r­w¸¸R½Õ/?Ó(@À2Õ(EÐEÐEr7   c                óœ   € R V,          \         P                  ! RV,          4      ,
          \        P                  ! R V,          4      ,           # r‘  r_  ©rD   r©  s   &&r5   r  Úgennorm_gen._entropy-  s0   € Ø�D�yœ2Ÿ6š6 " t¥)Ó,Õ,¬r¯zªz¸"¸t½)Ó/DÕDÐDr7   Nc                óÚ   € VP                  ^V,          VR7      pV^V,          ,          p\        P                  ! V4      pVP                  VP                  R7      R8  pWV,          ) WV&   V# )rM   r³  r£   )r(  rQ   r#  ÚrandomrG  )rD   r©  rô   rõ   rÓ  rv  r¼  s   &&&&   r5   rö   Úgennorm_gen._rvs-  sc   € ð ×Ñ˜q �v¨DÐÓ1ˆØ�!�D•&�Mˆä�JŠJ�q‹MˆØ×"Ñ"¨¯©Ð"Ó0°3Ñ6ˆØ•7�(ˆ‰Øˆr7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   ru   rý   ry   r„   r~   rˆ   r,  r   r  rö   r‘   r’   r“   s   @r5   r`  r`  ¼,  sM   ø‡ € ñ)òTHò-òFòDò
Nò
#ò#òòFòE÷	ò 	r7   r`  Úgennormc                   óT   a € ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tRtV tR# )Úhalfgennorm_geni-  aY  The upper half of a generalized normal continuous random variable.

%(before_notes)s

See Also
--------
gennorm : generalized normal distribution
expon : exponential distribution
halfnorm : half normal distribution

Notes
-----
The probability density function for `halfgennorm` is:

.. math::

    f(x, \beta) = \frac{\beta}{\Gamma(1/\beta)} \exp(-|x|^\beta)

for :math:`x, \beta > 0`. :math:`\Gamma` is the gamma function
(`scipy.special.gamma`).

`halfgennorm` takes ``beta`` as a shape parameter for :math:`\beta`.
For :math:`\beta = 1`, it is identical to an exponential distribution.
For :math:`\beta = 2`, it is identical to a half normal distribution
(with ``scale=1/sqrt(2)``).

References
----------

.. [1] "Generalized normal distribution, Version 1",
       https://en.wikipedia.org/wiki/Generalized_normal_distribution#Version_1

%(example)s

c                ó@   € \        R R^ \        P                  3R4      .# rb  rj   rl   s   &r5   rm   Úhalfgennorm_gen._shape_infoC-  rd  r7   c                óL   € \         P                  ! V P                  W4      4      # rO   r.  rf  s   &&&r5   ru   Úhalfgennorm_gen._pdfF-  s   € ô �vŠv�d—l‘l 1Ó+Ó,Ð,r7   c                óŒ   € \         P                  ! V4      \        P                  ! R V,          4      ,
          W,          ,
          # r8  r_  rf  s   &&&r5   rý   Úhalfgennorm_gen._logpdfL-  s)   € Ü�vŠv�d‹|œbŸjšj¨¨T­Ó2Õ2°QµWÕ<Ð<r7   c                óJ   € \         P                  ! R V,          W,          4      # r8  rA  rf  s   &&&r5   ry   Úhalfgennorm_gen._cdfO-  s   € Ü�{Š{˜3˜t�8 Q¥WÓ-Ð-r7   c                óZ   € \         P                  ! R V,          V4      R V,          ,          # r8  r~  rf  s   &&&r5   r„   Úhalfgennorm_gen._ppfR-  s    € Ü�~Š~˜c $�h¨Ó*¨S°­XÕ6Ð6r7   c                óJ   € \         P                  ! R V,          W,          4      # r8  rE  rf  s   &&&r5   r~   Úhalfgennorm_gen._sfU-  s   € Ü�|Š|˜C �H a¥gÓ.Ð.r7   c                óZ   € \         P                  ! R V,          V4      R V,          ,          # r8  r’  rf  s   &&&r5   rˆ   Úhalfgennorm_gen._isfX-  s    € Ü�Š˜s 4�x¨Ó+¨c°$­hÕ7Ð7r7   c                óŽ   € R V,          \         P                  ! V4      ,
          \        P                  ! R V,          4      ,           # r8  r_  r}  s   &&r5   r  Úhalfgennorm_gen._entropy[-  s+   € Ø�4�xœ"Ÿ&š& ›,Õ&¬¯ª°C¸µHÓ)=Õ=Ð=r7   r‹   Nrk  r“   s   @r5   r„  r„  -  s9   ø‡ € ñ"òFHò-ò=ò.ò7ò/ò8÷>ð >r7   r„  Úhalfgennormc                   óf   a a€ ] tR tRt oRtR tR tV 3R ltR tR t	R t
R	 tR
 tR tRtVtV ;t# )Úcrystalball_genib-  aY  
Crystalball distribution

%(before_notes)s

Notes
-----
The probability density function for `crystalball` is:

.. math::

    f(x, \beta, m) =  \begin{cases}
                        N \exp(-x^2 / 2),  &\text{for } x > -\beta\\
                        N A (B - x)^{-m}  &\text{for } x \le -\beta
                      \end{cases}

where :math:`A = (m / |\beta|)^m  \exp(-\beta^2 / 2)`,
:math:`B = m/|\beta| - |\beta|` and :math:`N` is a normalisation constant.

`crystalball` takes :math:`\beta > 0` and :math:`m > 1` as shape
parameters.  :math:`\beta` defines the point where the pdf changes
from a power-law to a Gaussian distribution.  :math:`m` is the power
of the power-law tail.

%(after_notes)s

.. versionadded:: 0.19.0

References
----------
.. [1] "Crystal Ball Function",
       https://en.wikipedia.org/wiki/Crystal_Ball_function

%(example)s
c                ó    € V^8„  V^ 8„  ,          # )z0
Shape parameter bounds are m > 1 and beta > 0.
r‹   )rD   r©  rì  s   &&&r5   rd   Úcrystalball_gen._argcheck†-  s   € ð �A‘˜$ ™(Õ#Ð#r7   c                ó€   € \        R R^ \        P                  3R4      p\        RR^\        P                  3R4      pW.# )r©  Frì  r4  rj   )rD   ÚibetaÚims   &  r5   rm   Úcrystalball_gen._shape_infoŒ-  s:   € Ü˜6 5¨1¬b¯f©f¨+°~ÓFˆÜ˜˜U Q¬¯© K°Ó@ˆØˆ{Ðr7   c                ó&   <€ \         SV `  VRR7      # )rM   r…  rG  ra  rb  s   &&€r5   r×  Úcrystalball_gen._fitstart‘-  s   ø€ ä‰wÑ  ¨HÐ Ó5Ð5r7   c                ó  € RW2,          V^,
          ,          \         P                  ! V^,          ) R,          4      ,          \        \        V4      ,          ,           ,          pR pR pV\        P
                  ! W) 8„  WV3WV4      ,          # )a(  
Return PDF of the crystalball function.

                                    --
                                   | exp(-x**2 / 2),  for x > -beta
crystalball.pdf(x, beta, m) =  N * |
                                   | A * (B - x)**(-m), for x <= -beta
                                    --
r–   rÒ   c                 óL   € \         P                  ! V ^,          ) ^,          4      # rD  r7  ©rt   r©  rì  s   &&&r5   ÚrhsÚ!crystalball_gen._pdf.<locals>.rhs¢-  s   € Ü—6’6˜1˜a�4˜% !�)Ó$Ð$r7   c                 óº   € W!,          V,          \         P                  ! V^,          ) R,          4      ,          W!,          V,
          V ,
          V) ,          ,          # rÐ   r7  r¢  s   &&&r5   ÚlhsÚ!crystalball_gen._pdf.<locals>.lhs¥-  sB   € Ø•V˜a•K¤"§&¢&¨$°­'¨°C­Ó"8Õ8Ø•V˜d•] QÕ&¨1¨"Õ-õ.ð /r7   ©rQ   rÓ   rÔ   rÜ   r  r  ©rD   rt   r©  rì  rñ  r£  r¦  s   &&&&   r5   ru   Úcrystalball_gen._pdf•-  so   € ð �1•6˜Q˜q�S•>¤B§F¢F¨D°!­G¨8°c­>Ó$:Õ:Ü¤¨4£Õ0õ1õ 2ˆò	%ò	/ð ”3—?’? 1 u¡9¨q¸¨l¸CÓEÕEÐEr7   c                óB  € RW2,          V^,
          ,          \         P                  ! V^,          ) R,          4      ,          \        \        V4      ,          ,           ,          pR pR p\         P                  ! V4      \
        P                  ! W) 8„  WV3WV4      ,           # )z8
Return the log of the PDF of the crystalball function.
r–   rÒ   c                 ó$   € V ^,          ) ^,          # rD  r‹   r¢  s   &&&r5   r£  Ú$crystalball_gen._logpdf.<locals>.rhs²-  s   € Ø�q•D�5˜•7ˆNr7   c                 óÞ   € V\         P                  ! W!,          4      ,          V^,          ^,          ,
          V\         P                  ! W!,          V,
          V ,
          4      ,          ,
          # rD  rc  r¢  s   &&&r5   r¦  Ú$crystalball_gen._logpdf.<locals>.lhsµ-  sB   € Ø”R—V’V˜A�F“^Õ# d¨A¥g¨a¥iÕ/°!´B·F²F¸1½6ÀD½=È1Õ;LÓ4MÕ2MÕMÐMr7   )rQ   rÓ   rÔ   rÜ   r  r  r  r©  s   &&&&   r5   rý   Úcrystalball_gen._logpdf«-  sx   € ð �1•6˜Q˜q�S•>¤B§F¢F¨D°!­G¨8°c­>Ó$:Õ:Ü¤¨4£Õ0õ1õ 2ˆò	ò	Nô �vŠv�a‹yœ3Ÿ?š?¨1¨u©9°qÀ°lÀCÓMÕMÐMr7   c                ó  € RW2,          V^,
          ,          \         P                  ! V^,          ) R,          4      ,          \        \        V4      ,          ,           ,          pR pR pV\        P
                  ! W) 8„  WV3WV4      ,          # )z(
Return CDF of the crystalball function
r–   rÒ   c                 óÚ   € W!,          \         P                  ! V^,          ) R,          4      ,          V^,
          ,          \        \        V 4      \        V) 4      ,
          ,          ,           # rÐ   ©rQ   rÓ   rÔ   rÜ   r¢  s   &&&r5   r£  Ú!crystalball_gen._cdf.<locals>.rhsÁ-  sL   € Ø•VœrŸvšv t¨Q¥w h°¥nÓ5Õ5¸¸1½Õ=Ü¤9¨Q£<´)¸T¸EÓ2BÕ#BÕCõDð Er7   c                 óä   € W!,          V,          \         P                  ! V^,          ) R,          4      ,          W!,          V,
          V ,
          V) ^,           ,          ,          V^,
          ,          # rÐ   r7  r¢  s   &&&r5   r¦  Ú!crystalball_gen._cdf.<locals>.lhsÅ-  sR   € Ø•V˜a•K¤"§&¢&¨$°­'¨°C­Ó"8Õ8Ø•V˜d•] QÕ&¨1¨"¨Q­$Õ/õ0Ø34°Qµ3õ8ð 9r7   r¨  r©  s   &&&&   r5   ry   Úcrystalball_gen._cdfº-  sp   € ð �1•6˜Q˜q�S•>¤B§F¢F¨D°!­G¨8°c­>Ó$:Õ:Ü¤¨4£Õ0õ1õ 2ˆò	Eò	9ð ”3—?’? 1 u¡9¨q¸¨l¸CÓEÕEÐEr7   c                óP   a € R pV 3R lp\         P                  ! W) 8„  WV3WE4      # )z4
Survival function of the crystalball distribution.
c                 óò   € W!,          V^,
          ,          \         P                  ! V^,          ) ^,          4      ,          \        \        V4      ,          ,           p\        \	        V 4      ,          V,          # r_   )rQ   rÓ   rÔ   rÜ   ræ   )rt   r©  rì  ÚMs   &&& r5   r£  Ú crystalball_gen._sf.<locals>.rhsÐ-  sK   € à•˜˜A�•œrŸvšv t¨Q¥w h¨q¥jÓ1Õ1´KÄ	È$ÃÕ4OÕOˆAÜœx¨›{Õ*¨1Õ,Ð,r7   c                 ó6   <€ ^SP                  WV4      ,
          # r_   r×	  )rt   r©  rì  rD   s   &&&€r5   r¦  Ú crystalball_gen._sf.<locals>.lhsÕ-  s   ø€ à�t—y‘y ¨!Ó,Õ,Ð,r7   r=  )rD   rt   r©  rì  r£  r¦  s   f&&&  r5   r~   Úcrystalball_gen._sfË-  s*   ø€ ò
	-õ
	-ô �Š˜q 5™y¨1°A¨,¸ÓAÐAr7   c                ó˜  € R W2,          V^,
          ,          \         P                  ! V^,          ) R,          4      ,          \        \        V4      ,          ,           ,          pWCV,          ,          \         P                  ! V^,          ) ^,          4      ,          V^,
          ,          pR pR p\        P
                  ! W8  WV3Wg4      # )r–   rÒ   c                 ó†  € \         P                  ! V^,          ) ^,          4      pW!,          V,          V^,
          ,          p^V\        \        V4      ,          ,           ,          pW!,          V,
          V^,
          W!,          V) ,          ,          V,          V ,          V,          ^^V,
          ,          ,          ,
          # rD  r³  ©rH  r©  rì  Úeb2r  rñ  s   &&&   r5   Úppf_lessÚ&crystalball_gen._ppf.<locals>.ppf_lessà-  s‹   € Ü—&’&˜$ �'˜ !�Ó$ˆCØ•˜3• ! A¥#Õ&ˆAØ�1”{¤Y¨t£_Õ4Õ4Õ5ˆAØ•F˜T•MØ˜!•e˜a�f¨¨�^Õ+¨CÕ/°Õ1°!Õ3°q¸!¸A½#µwÕ?õ@ð Ar7   c                 óD  € \         P                  ! V^,          ) ^,          4      pW!,          V,          V^,
          ,          p^V\        \        V4      ,          ,           ,          p\	        \        V) 4      ^\        ,          W,          V,
          ,          ,           4      # rD  )rQ   rÓ   rÔ   rÜ   rã   rÁ  s   &&&   r5   Úppf_greaterÚ)crystalball_gen._ppf.<locals>.ppf_greaterç-  sl   € Ü—&’&˜$ �'˜ !�Ó$ˆCØ•˜3• ! A¥#Õ&ˆAØ�1”{¤Y¨t£_Õ4Õ4Õ5ˆAÜœY¨ uÓ-°´;µÀÅÀqÅÕ0IÕIÓJÐJr7   r¨  )rD   rH  r©  rì  rñ  ÚpbetarÃ  rÆ  s   &&&&    r5   r„   Úcrystalball_gen._ppfÛ-  s”   € Ø�1•6˜Q˜q�S•>¤B§F¢F¨D°!­G¨8°c­>Ó$:Õ:Ü¤¨4£Õ0õ1õ 2ˆà�t•V•œrŸvšv t¨Q¥w h¨q¥jÓ1Õ1°Q¸µUÕ;ˆò	Aò	Kô �Š˜q™y¨1°A¨,¸ÓNÐNr7   c           
     óŒ  € RW2,          V^,
          ,          \         P                  ! V^,          ) R,          4      ,          \        \        V4      ,          ,           ,          pR pV\        P
                  ! V^,           V8  WV3\         P                  ! V\         P                  .R7      \         P                  R7      ,          # )zB
Returns the n-th non-central moment of the crystalball function.
r–   rÒ   c                ó:  € W!,          V,          \         P                  ! V^,          ) R,          4      ,          pW!,          V,
          p^V ^,
          R,          ,          \        P                  ! V ^,           ^,          4      ,          RRV ,          \        P                  ! V ^,           ^,          V^,          ^,          4      ,          ,           ,          p\         P
                  ! VP                  4      p\        \        V 4      ^,           4       Fy  pV\        P                  ! W4      W@V,
          ,          ,          RV,          ,          W',
          ^,
          ,          W!,          V) V,           ^,           ,          ,          ,          pK{  	  W6,          V,           # )z_
Returns n-th moment. Defined only if n+1 < m
Function cannot broadcast due to the loop over n
rÒ   r–   r  )
rQ   rÓ   r|   r(  rB  rê  rG  rR  r+  Úbinom)rc   r©  rì  rè  ré  r£  r¦  rk  s   &&&     r5   rM  Ú*crystalball_gen._munp.<locals>.n_th_momentö-  s  € ð
 •˜!•œbŸfšf d¨A¥g X°¥^Ó4Õ4ˆAØ•˜•ˆAØ˜˜!�˜S•y•>¤B§H¢H¨a°­c°1­WÓ$5Õ5Ø˜2 �'¤B§K¢K°°1µ°aµ¸¸q½À1½Ó$EÕEÕEõGˆCä—(’(˜3Ÿ9™9Ó%ˆCÜœ3˜q›6 A�:Ö&�ØœŸš ›¨¨q­S­Õ1°R¸!µGÕ;¸q½uÀq½yÕIØ� A 2¨¥6¨A¥:Õ.õ/õ 0’ñ 'ð •7˜S•=Ð r7   r  r  )	rQ   rÓ   rÔ   rÜ   r  r  r  r   rk   )rD   rc   r©  rì  rñ  rM  s   &&&&  r5   r,  Úcrystalball_gen._munpï-  s�   € ð �1•6˜Q˜q�S•>¤B§F¢F¨D°!­G¨8°c­>Ó$:Õ:Ü¤¨4£Õ0õ1õ 2ˆò	!ð ”3—?’? 1 q¥5¨1¡9¨q¸¨lÜ#%§<¢<°ÄRÇZÁZÀLÔ#QÜ.0¯f©fô6õ 6ð 	6r7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   r×  ru   rý   ry   r~   r„   r,  r‘   r’   r  r   s   @@r5   r—  r—  b-  sB   ù‡ € ñ"òF$òõ
6òFò,NòFò"Bò O÷(6ò 6r7   r—  ÚcrystalballzA Crystalball Function)rš   Úlongnamec                óZ   € \         P                  ! RV ^,          ^,          4      ^,          # )a‘  
Utility function for the argus distribution used in the pdf, sf and
moment calculation.
Note that for all x > 0:
gammainc(1.5, x**2/2) = 2 * (_norm_cdf(x) - x * _norm_pdf(x) - 0.5).
This can be verified directly by noting that the cdf of Gamma(1.5) can
be written as erf(sqrt(x)) - 2*sqrt(x)*exp(-x)/sqrt(Pi).
We use gammainc instead of the usual definition because it is more precise
for small chi.
rS  rA  )re  s   &r5   Ú
_argus_phirÒ  .  s"   € ô �;Š;�s˜C �F 1�HÓ%¨Õ)Ð)r7   c                   ó\   a € ] tR tRt o RtR tR tR tR tR t	RR	 lt
RR
 ltR tRtV tR# )Ú	argus_geni.  aª  
Argus distribution

%(before_notes)s

Notes
-----
The probability density function for `argus` is:

.. math::

    f(x, \chi) = \frac{\chi^3}{\sqrt{2\pi} \Psi(\chi)} x \sqrt{1-x^2}
                 \exp(-\chi^2 (1 - x^2)/2)

for :math:`0 < x < 1` and :math:`\chi > 0`, where

.. math::

    \Psi(\chi) = \Phi(\chi) - \chi \phi(\chi) - 1/2

with :math:`\Phi` and :math:`\phi` being the CDF and PDF of a standard
normal distribution, respectively.

`argus` takes :math:`\chi` as shape a parameter. Details about sampling
from the ARGUS distribution can be found in [2]_.

%(after_notes)s

References
----------
.. [1] "ARGUS distribution",
       https://en.wikipedia.org/wiki/ARGUS_distribution
.. [2] Christoph Baumgarten "Random variate generation by fast numerical
       inversion in the varying parameter case." Research in Statistics,
       vol. 1, 2023. :doi:`10.1080/27684520.2023.2279060`

.. versionadded:: 0.19.0

%(example)s
c                ó@   € \        R R^ \        P                  3R4      .# )re  Fr4  rj   rl   s   &r5   rm   Úargus_gen._shape_infoD.  ó   € Ü˜5 %¨!¬R¯V©V¨°nÓEÐFÐFr7   c                óú  € \         P                  ! R R7      ;_uu_ 4        RW,          ,
          p^\         P                  ! V4      ,          \        ,
          \         P                  ! \	        V4      4      ,
          pV\         P                  ! V4      ,           R\         P
                  ! V) V,          4      ,          ,           V^,          V,          ^,          ,
          uuRRR4       #   + '       g   i     R# ; i)rl  rm  r–   r£   N)rQ   ro  r  rØ   rÒ  ré  )rD   rt   re  rv  rè  s   &&&  r5   rý   Úargus_gen._logpdfG.  s‹   € ä�[Š[ ×)Ö)Ø�a•c•	ˆAØ”"—&’&˜“+•¤Õ.´·²¼
À3»Ó1HÕHˆAØ”r—v’v˜a“y•= 3¤r§x¢x°°°1µ£~Õ#5Õ5¸¸Q½À½
ÀQ½ÕF÷ *×)×)Ó)ús    B>C)Ã)C:	c                óL   € \         P                  ! V P                  W4      4      # rO   r.  ©rD   rt   re  s   &&&r5   ru   Úargus_gen._pdfN.  s   € Ü�vŠv�d—l‘l 1Ó*Ó+Ð+r7   c                ó2   € R V P                  W4      ,
          # r8  r1	  rÛ  s   &&&r5   ry   Úargus_gen._cdfQ.  s   € Ø�T—X‘X˜aÓ%Õ%Ð%r7   c                ó˜   € \        V\        P                  ! ^V,
          ^V,           ,          4      ,          4      \        V4      ,          # r_   )rÒ  rQ   r'  rÛ  s   &&&r5   r~   Úargus_gen._sfT.  s0   € Ü˜#¤§¢¨¨Q­°°Qµ­Ó 8Õ8Ó9¼JÀs»OÕKÐKr7   Nc                óÔ  a	a
€ \         P                  ! V4      pVP                  ^8X  d   V P                  WVR7      pEM\	        VP
                  V4      w  po	\        \         P                  ! V4      4      p\         P                  ! V4      p\         P                  ! V.R.R..R7      o
S
P                  '       g�   \        ;QJ d,    . V	V
3R l\        \        V4      ) ^ 4       4       F  NK  	  5M%! V	V
3R l\        \        V4      ) ^ 4       4       4      pV P                  S
^ ,          VVR7      pVP                  V4      WG&   S
P                  4        K®  VR8X  d
   VR,          pV# )rM   )rÞ  rõ   rÉ  rÊ  rË  c              3   ó~   <"  € T F2  pSV,          '       g   SP                   V,          M
\        R 4      x € K4  	  R # 5irO   rÏ  rÑ  s   & €€r5   rD  Ú!argus_gen._rvs.<locals>.<genexpr>d.  rÕ  rÖ  r‹   )rQ   r#  rô   r×  r   rG  r+  rQ  rØ  rÙ  rÚ  rÛ  rR  rç  r°  rÜ  )rD   re  rô   rõ   rJ  rÝ  rÞ  rß  rI  rÒ  rÓ  s   &&&&     @@r5   rö   Úargus_gen._rvsW.  s%  ù€ Ü�jŠj˜‹oˆØ�8‰8�qŒ=Ø×"Ñ" 3Ø0<ð #ó >ŠCô # 3§9¡9¨dÓ3‰GˆC�ÜœRŸWšW S›\Ó*ˆJÜ—(’(˜4“.ˆCÜ—’˜C˜5Ø"/ Ø&0 \ Nô4ˆBð —k—k�kß”eõ ;Ü%*¬C°«I¨:°qÔ%9ó;—e‘eõ ;Ü%*¬C°«I¨:°qÔ%9ó;ó ;�à×$Ñ$ R¨¥U°zØ2>ð %ó @�àŸ9™9 S›>�‘Ø—‘–à�2Œ:Ø�b•'ˆCØˆ
r7   c                óˆ  € \        \        P                  ! V4      4      p\        \        P                  ! V4      4      p\        P
                  ! V4      p^ pW,          pVR8:  d½   V) ^,          p	Wu8  d«   WW,
          p
VP                  V
R7      pVP                  V
R7      pVR,          p\        P                  ! V4      W�,          8*  p\        P                  ! V4      pV^ 8”  g   Ky  \        P                  ! ^WÞ,          ,
          4      pVWgW,           % W,          pK°  EMŒVR8:  dô   \        P                  ! V) ^,          4      pWu8  dÏ   WW,
          p
VP                  V
R7      pVP                  V
R7      p^\        P                  ! V^V,
          ,          V,           4      ,          V,          pV^,          V,           ^ 8*  p\        P                  ! V4      pV^ 8”  g   K�  \        P                  ! ^WÞ,          ,           4      pVWgW,           % W,          pKÔ  M’Wu8  db   WW,
          p
VP                  RV
R7      pVV^,          8*  p\        P                  ! V4      pV^ 8”  g   KL  VV,          WgW,           % W,          pKg  \        P                  ! ^^V,          V,          ,
          4      p\        P                  ! Wd4      # )r   r£   r³  gÍÌÌÌÌÌü?rS  rv  )rÛ  rQ   ré  r+  rQ  rê  r´  r  rè  r'  rÓ   r…  r°  )rD   re  rÞ  rõ   rð  rñ  rt   rò  r7  r  rk  rµ  r  rÓ  r 	  r	  r)  ÚechirI  s   &&&&               r5   r×  Úargus_gen._rvs_scalaro.  s6  € ôh ”r—}’} ZÓ0Ó1ˆÜ”—’˜“Ó ˆÜ�HŠH�Q‹KˆØˆ	Ø�yˆØ�#Œ:Ø�˜•	ˆAØ”-Ø•M�Ø ×(Ñ(¨aÐ(Ó0�Ø ×(Ñ(¨aÐ(Ó0�Ø˜•H�äŸ&š& ›) q¥uÑ,�ÜŸVšV F›^�
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Ø –>Ø<=¸f½I�A Õ!7Ð9ØÕ+’IÜ—’˜˜A �E D�LÕ(Ó)ˆAä�zŠz˜!Ó$Ð$r7   c                óH  € \         P                  ! V\        R 7      p\        V4      p\         P                  ! \         P
                  ^,          4      V,          \        P                  ! ^V^,          ^,          4      ,          V,          p\         P                  ! V4      pVR8„  pW,          p^^V^,          ,          ,
          V\        V4      ,          W%,          ,          ,           WE&   W( ,          p. ROp\         P                  ! Wv4      WE( &   W4V^,          ,
          RR3# )r	  r!  N)	g„_1gªÛÖ¾r   gWB³éa¿r   g½p|R÷H?r   gE'«å�¡?r   gš™™™™™Ù?)rQ   r#  r  rÒ  r'  r  r|   rî  r7  rÖ   rØ
  )rD   re  r÷  rì  rz  r¼  r\  Úcoefs   &&      r5   r   Úargus_gen._statsÔ.  sÐ   € ô �jŠj˜¤EÔ*ˆÜ˜‹oˆÜ�GŠG”B—E‘E˜!•GÓ˜sÕ"¤R§V¢V¨A¨s°A­v°a­xÓ%8Õ8¸3Õ>ˆä�mŠm˜CÓ ˆØ�S‰yˆØ�IˆØ˜˜A˜q�D�•L 1¤y°£|Õ#3°cµiÕ#?Õ?ˆ‰	Ø��JˆÚKˆÜ—Z’Z Ó(ˆˆE‰
Ø˜˜1�•*˜d DÐ(Ð(r7   r‹   r.  )rŒ   r�   rŽ   r�   r�   rm   rý   ru   ry   r~   rö   r×  r   r‘   r’   r“   s   @r5   rÔ  rÔ  .  s=   ø‡ € ñ'òPGòGò,ò&òLôô0c%÷J)ð )r7   rÔ  ÚarguszAn Argus Function)rš   rÐ  r˜   r™   c                   ó€   a a€ ] tR tRt oRt]P                  tRR/V 3R lltR tR t	R t
R	 tR
 tV 3R ltRtVtV ;t# )Úrv_histogramiè.  a  
Generates a distribution given by a histogram.
This is useful to generate a template distribution from a binned
datasample.

As a subclass of the `rv_continuous` class, `rv_histogram` inherits from it
a collection of generic methods (see `rv_continuous` for the full list),
and implements them based on the properties of the provided binned
datasample.

Parameters
----------
histogram : tuple of array_like
    Tuple containing two array_like objects.
    The first containing the content of n bins,
    the second containing the (n+1) bin boundaries.
    In particular, the return value of `numpy.histogram` is accepted.

density : bool, optional
    If False, assumes the histogram is proportional to counts per bin;
    otherwise, assumes it is proportional to a density.
    For constant bin widths, these are equivalent, but the distinction
    is important when bin widths vary (see Notes).
    If None (default), sets ``density=True`` for backwards compatibility,
    but warns if the bin widths are variable. Set `density` explicitly
    to silence the warning.

    .. versionadded:: 1.10.0

Notes
-----
When a histogram has unequal bin widths, there is a distinction between
histograms that are proportional to counts per bin and histograms that are
proportional to probability density over a bin. If `numpy.histogram` is
called with its default ``density=False``, the resulting histogram is the
number of counts per bin, so ``density=False`` should be passed to
`rv_histogram`. If `numpy.histogram` is called with ``density=True``, the
resulting histogram is in terms of probability density, so ``density=True``
should be passed to `rv_histogram`. To avoid warnings, always pass
``density`` explicitly when the input histogram has unequal bin widths.

There are no additional shape parameters except for the loc and scale.
The pdf is defined as a stepwise function from the provided histogram.
The cdf is a linear interpolation of the pdf.

.. versionadded:: 0.19.0

Examples
--------

Create a scipy.stats distribution from a numpy histogram

>>> import scipy.stats
>>> import numpy as np
>>> data = scipy.stats.norm.rvs(size=100000, loc=0, scale=1.5,
...                             random_state=123)
>>> hist = np.histogram(data, bins=100)
>>> hist_dist = scipy.stats.rv_histogram(hist, density=False)

Behaves like an ordinary scipy rv_continuous distribution

>>> hist_dist.pdf(1.0)
0.20538577847618705
>>> hist_dist.cdf(2.0)
0.90818568543056499

PDF is zero above (below) the highest (lowest) bin of the histogram,
defined by the max (min) of the original dataset

>>> hist_dist.pdf(np.max(data))
0.0
>>> hist_dist.cdf(np.max(data))
1.0
>>> hist_dist.pdf(np.min(data))
7.7591907244498314e-05
>>> hist_dist.cdf(np.min(data))
0.0

PDF and CDF follow the histogram

>>> import matplotlib.pyplot as plt
>>> X = np.linspace(-5.0, 5.0, 100)
>>> fig, ax = plt.subplots()
>>> ax.set_title("PDF from Template")
>>> ax.hist(data, density=True, bins=100)
>>> ax.plot(X, hist_dist.pdf(X), label='PDF')
>>> ax.plot(X, hist_dist.cdf(X), label='CDF')
>>> ax.legend()
>>> fig.show()

ÚdensityNc               ó  <€ Wn         W n        \        V4      ^8w  d   \        R4      h\        P
                  ! V^ ,          4      V n        \        P
                  ! V^,          4      V n        \        V P                  4      ^,           \        V P                  4      8w  d   \        R4      hV P                  R,          V P                  RR ,
          V n        \        P                  ! V P                  V P                  ^ ,          4      '       * pVf+   V'       d#   Rp\        P                  ! V\        ^R7       RpM*V'       g#   V P                  V P                  ,          V n        V P                  \        \        P                  ! V P                  V P                  ,          4      4      ,          V n        \        P                  ! V P                  V P                  ,          4      V n        \        P"                  ! RV P                  R.4      V n        \        P"                  ! RV P                   .4      V n        V P                  ^ ,          ;VR	&   V n        V P                  R,          ;VR
&   V n        \(        SV `T  ! V/ VB  R# )aµ  
Create a new distribution using the given histogram

Parameters
----------
histogram : tuple of array_like
    Tuple containing two array_like objects.
    The first containing the content of n bins,
    the second containing the (n+1) bin boundaries.
    In particular, the return value of np.histogram is accepted.
density : bool, optional
    If False, assumes the histogram is proportional to counts per bin;
    otherwise, assumes it is proportional to a density.
    For constant bin widths, these are equivalent.
    If None (default), sets ``density=True`` for backward
    compatibility, but warns if the bin widths are variable. Set
    `density` explicitly to silence the warning.
z)Expected length 2 for parameter histogramzbNumber of elements in histogram content and histogram boundaries do not match, expected n and n+1.r  NzjBin widths are not constant. Assuming `density=True`.Specify `density` explicitly to silence this warning.r³  Tr•   r˜   r™   r  )Ú
_histogramÚ_densityrç  r"  rQ   r#  Ú_hpdfÚ_hbinsÚ_hbin_widthsÚallcloserµ  r¶  r·  r  rè  ÚcumsumÚ_hcdfÚhstackr˜   r™   r@   rˆ  )rD   Ú	histogramrî  rF   r²  Ú	bins_varyr¹  rØ  s   &&$*,  €r5   rˆ  Úrv_histogram.__init__F/  sÄ  ø€ ð& $ŒØŒÜˆy‹>˜QÔÜÐHÓIÐIÜ—Z’Z 	¨!¥Ó-ˆŒ
Ü—j’j ¨1¥Ó.ˆŒÜˆt�z‰z‹?˜QÕ¤# d§k¡kÓ"2Ô2Üð 3ó 4ð 4ð !ŸK™K¨�O¨d¯k©k¸#¸2Ð.>Õ>ˆÔÜŸš D×$5Ñ$5°t×7HÑ7HÈÕ7KÓLÔLˆ	ØŠ?ŸyðOˆGä�MŠM˜'¤>¸aÕ@Ø‰GßØŸ™ d×&7Ñ&7Õ7ˆDŒJà—Z‘Z¤%¬¯ª¨t¯z©z¸D×<MÑ<MÕ/MÓ(NÓ"OÕOˆŒ
Ü—Y’Y˜tŸz™z¨D×,=Ñ,=Õ=Ó>ˆŒ
Ü—Y’Y  T§Z¡Z°Ð5Ó6ˆŒ
Ü—Y’Y  T§Z¡ZÐ0Ó1ˆŒ
à#Ÿ{™{¨1�~Ð-ˆˆs‰�d”fØ#Ÿ{™{¨2�Ð.ˆˆs‰�d”fÜ‰Ò˜$Ð) &Ô)r7   c                ój   € V P                   \        P                  ! V P                  VRR7      ,          # )z
PDF of the histogram
r8	  )Úside)rò  rQ   Úsearchsortedró  r¿   s   &&r5   ru   Úrv_histogram._pdfv/  s$   € ð �z‰zœ"Ÿ/š/¨$¯+©+°q¸wÔGÕHÐHr7   c                óX   € \         P                  ! WP                  V P                  4      # )z#
CDF calculated from the histogram
)rQ   Úinterpró  r÷  r¿   s   &&r5   ry   Úrv_histogram._cdf|/  s   € ô �yŠy˜ŸK™K¨¯©Ó4Ð4r7   c                óX   € \         P                  ! WP                  V P                  4      # )z3
Percentile function calculated from the histogram
)rQ   r  r÷  ró  r¿   s   &&r5   r„   Úrv_histogram._ppf‚/  s   € ô �yŠy˜ŸJ™J¨¯©Ó4Ð4r7   c                óø   € V P                   R,          V^,           ,          V P                   RR V^,           ,          ,
          V^,           ,          p\        P                  ! V P                  ^R V,          4      # )z$Compute the n-th non-central moment.r  Nr  )ró  rQ   rè  rò  )rD   rc   Ú	integralss   && r5   r,  Úrv_histogram._munpˆ/  sY   € à—[‘[ •_ q¨¥sÕ+¨d¯k©k¸#¸2Ð.>ÀÀ1ÅÕ.EÕEÈ!ÈAÍ#ÕNˆ	Ü�vŠv�d—j‘j  2Ð&¨Õ2Ó3Ð3r7   c                óÒ   € V P                   ^R p\        P                  ! VR8„  V\        P                  RR7      p\        P
                  ! W,          V P                  ,          4      ) # )zCompute entropy of distributionr•   r  r  )rò  r  r  rQ   r  rè  rô  )rD   Úhpdfr›  s   &  r5   r  Úrv_histogram._entropy�/  sM   € à�z‰z˜!˜BÐˆÜ�oŠo˜d S™j¨$´·±À3ÔGˆÜ—’�t•z D×$5Ñ$5Õ5Ó6Ð6Ð6r7   c                ó`   <€ \         SV `  4       pV P                  VR&   V P                  VR&   V# )z6
Set the histogram as additional constructor argument
rù  rî  )r@   Ú_updated_ctor_paramrð  rñ  )rD   ÚdctrØ  s   & €r5   r  Ú rv_histogram._updated_ctor_param“/  s2   ø€ ô ‰gÑ)Ó+ˆØŸ?™?ˆˆKÑØŸ™ˆˆI‰Øˆ
r7   )rñ  rô  ró  r÷  rð  rò  r˜   r™   )rŒ   r�   rŽ   r�   r�   r   rJ  rˆ  ru   ry   r„   r,  r  r  r‘   r’   r  r   s   @@r5   rí  rí  è.  sJ   ù‡ € ñZðv "×/Ñ/€Mð.*°÷ .*ò`Iò5ò5ò4ò
7÷õ r7   rí  c                   óT   a a€ ] tR tRt oRtR tR tV 3R ltR tR t	R t
R	tVtV ;t# )
Ústudentized_range_geni�/  u  A studentized range continuous random variable.

%(before_notes)s

See Also
--------
t: Student's t distribution

Notes
-----
The probability density function for `studentized_range` is:

.. math::

     f(x; k, \nu) = \frac{k(k-1)\nu^{\nu/2}}{\Gamma(\nu/2)
                    2^{\nu/2-1}} \int_{0}^{\infty} \int_{-\infty}^{\infty}
                    s^{\nu} e^{-\nu s^2/2} \phi(z) \phi(sx + z)
                    [\Phi(sx + z) - \Phi(z)]^{k-2} \,dz \,ds

for :math:`x â‰¥ 0`, :math:`k > 1`, and :math:`\nu > 0`.

`studentized_range` takes ``k`` for :math:`k` and ``df`` for :math:`\nu`
as shape parameters.

When :math:`\nu` exceeds 100,000, an asymptotic approximation (infinite
degrees of freedom) is used to compute the cumulative distribution
function [4]_ and probability distribution function.

%(after_notes)s

References
----------

.. [1] "Studentized range distribution",
       https://en.wikipedia.org/wiki/Studentized_range_distribution
.. [2] Batista, Ben DÃªivide, et al. "Externally Studentized Normal Midrange
       Distribution." CiÃªncia e Agrotecnologia, vol. 41, no. 4, 2017, pp.
       378-389., doi:10.1590/1413-70542017414047716.
.. [3] Harter, H. Leon. "Tables of Range and Studentized Range." The Annals
       of Mathematical Statistics, vol. 31, no. 4, 1960, pp. 1122-1147.
       JSTOR, www.jstor.org/stable/2237810. Accessed 18 Feb. 2021.
.. [4] Lund, R. E., and J. R. Lund. "Algorithm AS 190: Probabilities and
       Upper Quantiles for the Studentized Range." Journal of the Royal
       Statistical Society. Series C (Applied Statistics), vol. 32, no. 2,
       1983, pp. 204-210. JSTOR, www.jstor.org/stable/2347300. Accessed 18
       Feb. 2021.

Examples
--------
>>> import numpy as np
>>> from scipy.stats import studentized_range
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Display the probability density function (``pdf``):

>>> k, df = 3, 10
>>> x = np.linspace(studentized_range.ppf(0.01, k, df),
...                 studentized_range.ppf(0.99, k, df), 100)
>>> ax.plot(x, studentized_range.pdf(x, k, df),
...         'r-', lw=5, alpha=0.6, label='studentized_range pdf')

Alternatively, the distribution object can be called (as a function)
to fix the shape, location and scale parameters. This returns a "frozen"
RV object holding the given parameters fixed.

Freeze the distribution and display the frozen ``pdf``:

>>> rv = studentized_range(k, df)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

Check accuracy of ``cdf`` and ``ppf``:

>>> vals = studentized_range.ppf([0.001, 0.5, 0.999], k, df)
>>> np.allclose([0.001, 0.5, 0.999], studentized_range.cdf(vals, k, df))
True

Rather than using (``studentized_range.rvs``) to generate random variates,
which is very slow for this distribution, we can approximate the inverse
CDF using an interpolator, and then perform inverse transform sampling
with this approximate inverse CDF.

This distribution has an infinite but thin right tail, so we focus our
attention on the leftmost 99.9 percent.

>>> a, b = studentized_range.ppf([0, .999], k, df)
>>> a, b
0, 7.41058083802274

>>> from scipy.interpolate import interp1d
>>> rng = np.random.default_rng()
>>> xs = np.linspace(a, b, 50)
>>> cdf = studentized_range.cdf(xs, k, df)
# Create an interpolant of the inverse CDF
>>> ppf = interp1d(cdf, xs, fill_value='extrapolate')
# Perform inverse transform sampling using the interpolant
>>> r = ppf(rng.uniform(size=1000))

And compare the histogram:

>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

c                ó    € V^8„  V^ 8„  ,          # r_   r‹   )rD   rk  r3  s   &&&r5   rd   Ústudentized_range_gen._argcheck0  s   € Ø�A‘˜"˜q™&Õ!Ð!r7   c                ó€   € \        R R^\        P                  3R4      p\        RR^ \        P                  3R4      pW.# )rk  Fr3  r4  rj   )rD   r,  rú  s   &  r5   rm   Ú!studentized_range_gen._shape_info0  s:   € Ü˜˜U Q¬¯© K°Ó@ˆÜ˜˜u q¬"¯&©& k°>ÓBˆØˆyÐr7   c                ó&   <€ \         SV `  VRR7      # )rÑ   r…  )rÑ   rM   ra  rb  s   &&€r5   r×  Ústudentized_range_gen._fitstart0  s   ø€ ä‰wÑ  ¨FÐ Ó3Ð3r7   c                óÚ   aaa€ R oV P                  4       w  ooVVV3R lp\        P                  ! V^^4      p\        P                  ! V! WV4      \        P                  R7      R,          # )Ú_studentized_range_momentc                 ó¸  <€ \         P                  ! W4      pWW#.p\        P                  ! V\        4      P
                  P                  \
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3.p\        RRR7      p\        P                  ! WgVR7      ^ ,          # )r   rw  çê-�™—q=©r%  r$  ©ÚrangesÚopts)r   Ú_studentized_range_pdf_logconstrQ   r&  r  r'  r(  r)  r   r*  rk   Údictr   Únquad)rX  rk  r3  Ú	log_constÚargÚusr_datar0  r  r  r   r  Úcython_symbols   &&&      €€€r5   Ú_single_momentÚ3studentized_range_gen._munp.<locals>._single_moment0  sŸ   ø€ Ü×>Ò>¸qÓEˆIØ˜Ð'ˆCÜ—x’x ¤UÓ+×2Ñ2×:Ñ:¼6¿?¹?ÓKˆHä"×.Ò.¬v°}ÀhÓOˆCäŸ™�w¤§¡Ð'¨!¬R¯V©V¨°r¸2°hÐ?ˆFÜ˜u¨UÔ3ˆDä—?’? 3¸DÔAÀ!ÕDÐDr7   r	  r‹   )r¥   rQ   Ú
frompyfuncr#  r   )	rD   rX  rk  r3  r&  Úufuncr   r  r%  s	   &&&&  @@@r5   r,  Ústudentized_range_gen._munp0  sT   ú€ Ø3ˆØ×"Ñ"Ó$‰ˆˆB÷
	Eô —’˜n¨a°Ó3ˆÜ�zŠz™%  b›/´·±Ô<¸RÕ@Ð@r7   c                ó    € R  p\         P                  ! V^^4      p\         P                  ! V! WV4      \         P                  R7      R,          # )c                 ó”  € VR 8  d“   Rp\         P                  ! W4      pWW$.p\        P                  ! V\        4      P
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        P                  4      p\        P                  ) \        P                  3.p\        P                  ! \         W64      p\        RRR7      p	\        P                  ! W‡V	R7      ^ ,          # )é † Ú_studentized_range_pdfÚ!_studentized_range_pdf_asymptoticrw  r  r  r  )r   r  rQ   r&  r  r'  r(  r)  rk   r   r*  r   r   r!  ©
rƒ   rk  r3  r%  r"  r#  r$  r  r0  r  s
   &&&       r5   Ú_single_pdfÚ/studentized_range_gen._pdf.<locals>._single_pdf+0  sï   € ð �FŒ{Ø 8�Ü"×BÒBÀ1ÓI�	Ø˜RÐ+�ÜŸ8š8 C¬Ó/×6Ñ6×>Ñ>¼v¿¹ÓO�ÜŸF™F˜7¤B§F¡FÐ+¨a´·±¨[Ð9‘ð !D�Ø�f�ÜŸ8š8 C¬Ó/×6Ñ6×>Ñ>¼v¿¹ÓO�ÜŸF™F˜7¤B§F¡FÐ+Ð,�ä"×.Ò.¬v°}ÓOˆCÜ˜u¨UÔ3ˆDÜ—?’? 3¸DÔAÀ!ÕDÐDr7   r	  r‹   )rQ   r(  r#  r   )rD   rt   rk  r3  r1  r)  s   &&&&  r5   ru   Ústudentized_range_gen._pdf)0  s<   € ò	Eô( —’˜k¨1¨aÓ0ˆÜ�zŠz™%  b›/´·±Ô<¸RÕ@Ð@r7   c           	     óÌ   € R  p\         P                  ! V^^4      p\         P                  ! \         P                  ! V! WV4      \         P                  R7      R,          ^ ^4      # )c                 ó”  € VR 8  d“   Rp\         P                  ! W4      pWW$.p\        P                  ! V\        4      P
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        P                  4      p\        P                  ) \        P                  3.p\        P                  ! \         W64      p\        RRR7      p	\        P                  ! W‡V	R7      ^ ,          # )r-  Ú_studentized_range_cdfÚ!_studentized_range_cdf_asymptoticrw  r  r  r  )r   Ú_studentized_range_cdf_logconstrQ   r&  r  r'  r(  r)  rk   r   r*  r   r   r!  r0  s
   &&&       r5   Ú_single_cdfÚ/studentized_range_gen._cdf.<locals>._single_cdfD0  sï   € ð
 �FŒ{Ø 8�Ü"×BÒBÀ1ÓI�	Ø˜RÐ+�ÜŸ8š8 C¬Ó/×6Ñ6×>Ñ>¼v¿¹ÓO�ÜŸF™F˜7¤B§F¡FÐ+¨a´·±¨[Ð9‘ð !D�Ø�f�ÜŸ8š8 C¬Ó/×6Ñ6×>Ñ>¼v¿¹ÓO�ÜŸF™F˜7¤B§F¡FÐ+Ð,�ä"×.Ò.¬v°}ÓOˆCÜ˜u¨UÔ3ˆDÜ—?’? 3¸DÔAÀ!ÕDÐDr7   r	  r‹   )rQ   r(  rž  r#  r   )rD   rt   rk  r3  r9  r)  s   &&&&  r5   ry   Ústudentized_range_gen._cdfB0  sK   € ò	Eô, —’˜k¨1¨aÓ0ˆô �wŠw”r—z’z¡%¨¨b£/¼¿¹ÔDÀRÕHÈ!ÈQÓOÐOr7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   r×  r,  ru   ry   r‘   r’   r  r   s   @@r5   r  r  �/  s3   ù‡ € ñhòT"òõ
4òAò*A÷2Pò Pr7   r  Ústudentized_range)rš   r˜   r™   c                   óp   a a€ ] tR tRt oRtR tR tR tR tR t	R t
]! ]4      V 3R	 l4       tR
tVtV ;t# )Úrel_breitwigner_genid0  aO  A relativistic Breit-Wigner random variable.

%(before_notes)s

See Also
--------
cauchy: Cauchy distribution, also known as the Breit-Wigner distribution.

Notes
-----

The probability density function for `rel_breitwigner` is

.. math::

    f(x, \rho) = \frac{k}{(x^2 - \rho^2)^2 + \rho^2}

where

.. math::
    k = \frac{2\sqrt{2}\rho^2\sqrt{\rho^2 + 1}}
        {\pi\sqrt{\rho^2 + \rho\sqrt{\rho^2 + 1}}}

The relativistic Breit-Wigner distribution is used in high energy physics
to model resonances [1]_. It gives the uncertainty in the invariant mass,
:math:`M` [2]_, of a resonance with characteristic mass :math:`M_0` and
decay-width :math:`\Gamma`, where :math:`M`, :math:`M_0` and :math:`\Gamma`
are expressed in natural units. In SciPy's parametrization, the shape
parameter :math:`\rho` is equal to :math:`M_0/\Gamma` and takes values in
:math:`(0, \infty)`.

Equivalently, the relativistic Breit-Wigner distribution is said to give
the uncertainty in the center-of-mass energy :math:`E_{\text{cm}}`. In
natural units, the speed of light :math:`c` is equal to 1 and the invariant
mass :math:`M` is equal to the rest energy :math:`Mc^2`. In the
center-of-mass frame, the rest energy is equal to the total energy [3]_.

%(after_notes)s

:math:`\rho = M/\Gamma` and :math:`\Gamma` is the scale parameter. For
example, if one seeks to model the :math:`Z^0` boson with :math:`M_0
\approx 91.1876 \text{ GeV}` and :math:`\Gamma \approx 2.4952\text{ GeV}`
[4]_ one can set ``rho=91.1876/2.4952`` and ``scale=2.4952``.

To ensure a physically meaningful result when using the `fit` method, one
should set ``floc=0`` to fix the location parameter to 0.

References
----------
.. [1] Relativistic Breit-Wigner distribution, Wikipedia,
       https://en.wikipedia.org/wiki/Relativistic_Breit-Wigner_distribution
.. [2] Invariant mass, Wikipedia,
       https://en.wikipedia.org/wiki/Invariant_mass
.. [3] Center-of-momentum frame, Wikipedia,
       https://en.wikipedia.org/wiki/Center-of-momentum_frame
.. [4] M. Tanabashi et al. (Particle Data Group) Phys. Rev. D 98, 030001 -
       Published 17 August 2018

%(example)s

c                ó   € V^ 8„  # r  r‹   ©rD   Úrhos   &&r5   rd   Úrel_breitwigner_gen._argcheck¢0  s   € Ø�Q‰wˆr7   c                ó@   € \        R R^ \        P                  3R4      .# )rA  Fr4  rj   rl   s   &r5   rm   Úrel_breitwigner_gen._shape_info¥0  r×  r7   c           
     óê  € \         P                  ! ^^^V^,          ,          ,           ,          ^\         P                  ! ^^V^,          ,          ,           4      ,           ,          4      ^,          \         P                  ,          p\         P                  ! RR7      ;_uu_ 4        W1V,
          W,           ,          V,          ^,          ^,           ,          uuRRR4       #   + '       g   i     R# ; i)rÑ   rl  r­  N)rQ   r'  r  ro  )rD   rt   rA  r  s   &&& r5   ru   Úrel_breitwigner_gen._pdf¨0  s—   € ä�GŠGØ��Q�s˜A•v•X•Õ !¤b§g¢g¨a°!°C¸µFµ(­lÓ&;Õ";Õ<ó
àõä—‘õˆô �[Š[˜h×'Ö'Ø˜c�' A¥GÕ,¨SÕ0°1Õ4°qÕ8Õ9÷ (×'×'Ó'ús   Â%1C!Ã!C2	c           
     ó  € \         P                  ! ^^\         P                  ! ^^V^,          ,          ,           4      ,           ,          4      \         P                  ,          p\         P                  ! RRV,          ,           4      \         P                  ! V\         P                  ! V) VR,           ,          4      ,          4      ,          pV^,          \         P                  ! V4      ,          p\         P
                  ! VR^4      # )rÑ   rÿ  Nr  )rQ   r'  r  rÜ  Úimagrž  )rD   rt   rA  r  r+	  s   &&&  r5   ry   Úrel_breitwigner_gen._cdf°0  s¥   € ä�GŠG�A�qœ2Ÿ7š7 1 q¨¨a­¥x¥<Ó0Õ0Õ1Ó2´2·5±5Õ8ˆä�GŠG�B˜˜C�•KÓ Ü�iŠi˜œ"Ÿ'š' 3 $¨¨b­¥/Ó2Õ2Ó3õ4ð 	ð �Q•œŸš ›Õ(ˆä�wŠw�v˜t QÓ'Ð'r7   c                óf  € V^ 8X  d   R# V^8X  d¿   \         P                  ! ^^^V^,          ,          ,           ,          ^\         P                  ! ^^V^,          ,          ,           4      ,           ,          4      \         P                  ,          V,          pV\         P                  ^,          \         P                  ! V4      ,           ,          # V^8X  dÎ   \         P                  ! ^^V^,          ,          ,           ^^\         P                  ! ^^V^,          ,          ,           4      ,           ,          ,          4      V,          p^VR,          ,
          \         P                  ! RRV,          ,
          4      ,          p^V,          \         P                  ! V4      ,          # \         P
                  # )r   r–   rÿ  r  )rQ   r'  r  rÜ  r  rk   )rD   rc   rA  r  r+	  s   &&&  r5   r,  Úrel_breitwigner_gen._munp»0  s  € Ø�Œ6ÙØ�Œ6ä—’Ø�Q˜˜3 �6�•\Õ" a¬"¯'ª'°!°a¸¸Q½µhµ,Ó*?Õ&?Õ@óä—‘õàõˆAð œŸ™˜a�¤"§)¢)¨C£.Õ0Õ1Ð1Ø�Œ6ä—’Ø�Q�s˜A•v•X• ! q¬2¯7ª7°1°q¸¸a½µxµ<Ó+@Õ'@Õ"AÕBóàõˆAð ˜# �(•l¤b§g¢g¨b°2°cµ6­kÓ&:Õ:ˆFØ�q•5œ2Ÿ7š7 6›?Õ*Ð*ä—6‘6ˆMr7   c                óF   € R R \         P                  \         P                  3# rO   r  r@  s   &&r5   r   Úrel_breitwigner_gen._statsÎ0  s   € ð �Tœ2Ÿ6™6¤2§6¡6Ð)Ð)r7   c                óø  <€ \        WW#4      w  rrV\        V\        4      pV'       d$   VP                  4       ^ 8X  d   VP                  pRpVe	   V'       d   \
        SV `  ! V.VO5/ VB # VfJ   \        P                  ! W,
          . RO4      w  r‰p
W¨,
          pW›,          pV'       g   V.pRV9  d   W³R&   M/\        P                  ! W,
          4      pWÖ,          pV'       g   V.p\
        SV `  ! V.VO5/ VB # )r   Fr.   )r¼  r£   g      è?)
rR  r>   r)   r?   rC   r@   rB   rQ   Úquantilerã	  )rD   rE   rF   r4   r  r  r  rG   r)  r*  r+  Úscale_0Úrho_0ÚM_0rØ  s   &&*,          €r5   rB   Úrel_breitwigner_gen.fitÔ0  sí   ø€ ô !<Ø˜ó!
Ñˆ�ô ˜d¤LÓ1ˆßØ× Ñ Ó" aÔ'ð ×'Ñ'�Ø �àŠ<Ÿ8Ü‘7’;˜tÐ3 dÒ3¨dÑ3Ð3àŠ>ô ŸKšK¨­Ò5FÓG‰MˆC�cØ•iˆGØ•MˆEßØ�w�Ø˜dÔ"Ø '�W‘øä—)’)˜D�KÓ(ˆCØ•LˆEßØ�w�Ü‰wŠ{˜4Ð/ $Ò/¨$Ñ/Ð/r7   r‹   )rŒ   r�   rŽ   r�   r�   rd   rm   ru   ry   r,  r   r   r   rB   r‘   r’   r  r   s   @@r5   r>  r>  d0  sH   ù‡ € ñ<òzòGò:ò	(òò&*ñ ˜MÓ*ô 0ó +÷ 0ð  0r7   r>  Úrel_breitwignerrO   rò  r›  )r•   rc   )r•   r™   )r–   r\  (N  rµ  Úcollections.abcr   Ú	functoolsr   r   r'  r/  ÚnumpyrQ   Únumpy.polynomialr   Úscipy.interpolater   Úscipy._lib.doccerr	   r
   r   Úscipy._lib._ccallbackr   Úscipyr   r   Úscipy.specialÚspecialr|   Úscipy.special._ufuncsrh  rq   Úscipy._lib._utilr   Úscipy._lib.array_api_extraÚ_libÚarray_api_extrar  Úscipy._lib._array_apir   rŽ  r   Ú_tukeylambda_statsr   rÖ  r   r×  Ú_distn_infrastructurer   r   r   r   r   r   r   r   r   Ú_ksstatsr   r   r    Ú
_constantsr!   r"   r#   r$   r%   r&   r'   r(   Ú_censored_datar)   Úscipy.optimizer*   Úscipy.stats._warnings_errorsr+   Úscipy.statsrF  r6   rK   r[   r]   r—   rœ   r¶   r¹   rÎ   r'  r  rÔ   r  rØ   rÖ   rÙ   rÜ   rß   rã   ræ   ré   rì   rî   r/  r1  rK  rM  rf  rh  r�  r"  rƒ  rX   r™  r�  rŸ  r©  r"  rW  rY  rs  ru  r¾  rÀ  rÝ  rß  rü  rþ  r.  r0  re  rg  r7  r�  r¬  r®  rÌ  rÎ  r	  r  r/  r1  rQ  rV  rs  rw  ry  r�  r’  r«  r­  rÊ  rÌ  rã  rå  rœ  r  r&  r(  r  rY  r†  Ú_supportrˆ  r�  rŸ  rÁ  rÃ  rý  rÿ  r  r  rq  r~  r€  r(  r±  rÂ  rÄ  rï  rñ  r  r  rU  rW  rl  rr  rt  r�  rŸ  r»  r½  rÔ  rç  r  r  r.  r4  rH  rJ  rW  rY  r{  r}  r¤  r¬  r<  r	  rE	  rG	  r^	  r`	  r{	  r}	  r�	  r‘	  r¨	  rª	  rÊ	  rÌ	  rÐ	  ræ	  r
  rR  r
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  r=
  r?
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