+
    LV-jëI  ã                   ó”  € ^ RI t ^ RIt^ RIHt ^ RIHt ^ RIHt ^ RI	H
t ^ RIHtHtHtHtHtHtHt . ROt ! R R]4      tR t ! R R]4      t ! R R]4      t ! R R]4      t ! R R	]4      t ! R R]4      t ! R R
]4      t] P:                  ],          P>                  t ] F  t!]! ] ]!,          4      ] ]!,          n"        K   	  R# )é    N)Úinf)Úarray_api_extra)Úspecial)Ú_ufuncs)ÚContinuousDistributionÚDiscreteDistributionÚ_RealIntervalÚ_IntegerIntervalÚ_RealParameterÚ_ParameterizationÚ_combine_docsÚNormalÚLogisticÚUniformÚBinomialc                   ó  a a€ ] tR t^t oRt]! ]) ]3R7      t]! ^ ]3R7      t]! ]) ]3R7      t	]
! RR]R R7      t]
! RR]R!R7      t]
! R]	R R	7      t]! ]]4      .t]t^]P$                  ! ^]P&                  ,          4      ,          t]P*                  ! ^]P&                  ,          4      ^,          tR"V 3R
 lltRRRR/V 3R lltR tR tR tR tR tR tR tR t R t!R t"R t#R t$R t%R t&R t'^ ^.]'n(        R t)R t*Rt+Vt,V ;t-# )#r   a  Normal distribution with prescribed mean and standard deviation.

The probability density function of the normal distribution is:

.. math::

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

©Ú	endpointsÚmuz\mu©ÚsymbolÚdomainÚtypicalÚsigmaz\sigmaÚx©r   r   c                óX   <€ Vf   Vf   \         SV `  \        4      # \         SV `  V 4      # ©N)ÚsuperÚ__new__ÚStandardNormal)Úclsr   r   ÚkwargsÚ	__class__s   &&&,€Úo/Volumes/fast/ai/experiments/ui-tars-smoke/.venv/lib/python3.14/site-packages/scipy/stats/_new_distributions.pyr    ÚNormal.__new__.   s*   ø€ ØŠ:˜%š-Ü‘7‘?¤>Ó2Ð2Ü‰w‰˜sÓ#Ð#ó    ç        ç      ð?c               ó0   <€ \         SV `  ! RR VRV/VB  R# )r   r   N© ©r   Ú__init__)Úselfr   r   r#   r$   s   &$$,€r%   r-   ÚNormal.__init__3   s   ø€ Ü‰ÒÑ6˜BÐ6 eÐ6¨vÔ6r'   c               ó~   € \         P                  WV,
          V,          4      \        P                  ! V4      ,
          # r   )r!   Ú_logpdf_formulaÚnpÚlog©r.   r   r   r   r#   s   &&$$,r%   r1   ÚNormal._logpdf_formula6   s(   € Ü×-Ñ-¨d¸µV¸UµNÓCÄbÇfÂfÈUÃmÕSÐSr'   c               óV   € \         P                  WV,
          V,          4      V,          # r   )r!   Ú_pdf_formular4   s   &&$$,r%   r7   ÚNormal._pdf_formula9   s    € Ü×*Ñ*¨4°bµ&¸%µÓ@À5ÕHÐHr'   c               óH   € \         P                  WV,
          V,          4      # r   )r!   Ú_logcdf_formular4   s   &&$$,r%   r:   ÚNormal._logcdf_formula<   s   € Ü×-Ñ-¨d¸µV¸UµNÓCÐCr'   c               óH   € \         P                  WV,
          V,          4      # r   )r!   Ú_cdf_formular4   s   &&$$,r%   r=   ÚNormal._cdf_formula?   s   € Ü×*Ñ*¨4°bµ&¸%µÓ@Ð@r'   c               óH   € \         P                  WV,
          V,          4      # r   )r!   Ú_logccdf_formular4   s   &&$$,r%   r@   ÚNormal._logccdf_formulaB   s   € Ü×.Ñ.¨t¸"µf¸eµ^ÓDÐDr'   c               óH   € \         P                  WV,
          V,          4      # r   )r!   Ú_ccdf_formular4   s   &&$$,r%   rC   ÚNormal._ccdf_formulaE   s   € Ü×+Ñ+¨D°rµ6¸5µ.ÓAÐAr'   c               óH   € \         P                  W4      V,          V,           # r   )r!   Ú_icdf_formular4   s   &&$$,r%   rF   ÚNormal._icdf_formulaH   s   € Ü×+Ñ+¨DÓ4°uÕ<¸rÕAÐAr'   c               óH   € \         P                  W4      V,          V,           # r   )r!   Ú_ilogcdf_formular4   s   &&$$,r%   rI   ÚNormal._ilogcdf_formulaK   s   € Ü×.Ñ.¨tÓ7¸%Õ?À"ÕDÐDr'   c               óH   € \         P                  W4      V,          V,           # r   )r!   Ú_iccdf_formular4   s   &&$$,r%   rL   ÚNormal._iccdf_formulaN   s   € Ü×,Ñ,¨TÓ5¸Õ=ÀÕBÐBr'   c               óH   € \         P                  W4      V,          V,           # r   )r!   Ú_ilogccdf_formular4   s   &&$$,r%   rO   ÚNormal._ilogccdf_formulaQ   s   € Ü×/Ñ/°Ó8¸5Õ@À2ÕEÐEr'   c               ót   € \         P                  V 4      \        P                  ! \	        V4      4      ,           # r   )r!   Ú_entropy_formular2   r3   Úabs©r.   r   r   r#   s   &$$,r%   rR   ÚNormal._entropy_formulaT   s%   € Ü×.Ñ.¨tÓ4´r·v²v¼cÀ%»jÓ7IÕIÐIr'   c          	     óp  € \         P                  V 4      p\        P                  ! R R7      ;_uu_ 4        \        P                  ! \        P                  ! \        V4      4      R,           4      pRRR4       \        P                  ! \        P                  ! VX4      ^ R7      #   + '       g   i     L=; i)Úignore©Údividey                N©Úaxis)	r!   Ú_logentropy_formular2   Úerrstater3   rS   r   Ú	logsumexpÚbroadcast_arrays)r.   r   r   r#   ÚlH0Úllss   &$$,  r%   r\   ÚNormal._logentropy_formulaW   ss   € Ü×0Ñ0°Ó6ˆÜ�[Š[ ×)Ö)ô —&’&œŸš¤ E£
Ó+¨BÕ.Ó/ˆC÷ *ô × Ò ¤×!4Ò!4°S¸#Ó!>ÀQÔGÐG÷	 *×)ús   µ;B%Â%B5	c               ó   € V# r   r+   rT   s   &$$,r%   Ú_median_formulaÚNormal._median_formula_   ó   € Øˆ	r'   c               ó   € V# r   r+   rT   s   &$$,r%   Ú_mode_formulaÚNormal._mode_formulab   rf   r'   c               óR   € V^ 8X  d   \         P                  ! V4      # V^8X  d   V# R# ©r   N)r2   Ú	ones_like©r.   Úorderr   r   r#   s   &&$$,r%   Ú_moment_raw_formulaÚNormal._moment_raw_formulae   s'   € Ø�AŒ:Ü—<’< Ó#Ð#Ø�aŒZØˆIár'   c               óð   € V^ 8X  d   \         P                  ! V4      # V^,          '       d   \         P                  ! V4      # W1,          \        P                  ! \        V4      ^,
          RR7      ,          # )r   T)Úexact)r2   rl   Ú
zeros_liker   Ú
factorial2Úintrm   s   &&$$,r%   Ú_moment_central_formulaÚNormal._moment_central_formulan   sT   € Ø�AŒ:Ü—<’< Ó#Ð#Ø�Q�YŒYÜ—=’= Ó$Ð$ð •<¤'×"4Ò"4´S¸³ZÀ!µ^È4Ô"PÕPÐPr'   c               ó6   € VP                  W4VR 7      R,          # ))ÚlocÚscaleÚsizer+   ©Únormal)r.   Ú
full_shapeÚrngr   r   r#   s   &&&$$,r%   Ú_sample_formulaÚNormal._sample_formulaw   s   € Ø�z‰z˜b°JˆzÓ?ÀÕCÐCr'   r+   )éÿÿÿÿé   )ç      à?g      ø?)NN).Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__doc__r	   r   Ú
_mu_domainÚ_sigma_domainÚ
_x_supportr   Ú	_mu_paramÚ_sigma_paramÚ_x_paramr   Ú_parameterizationsÚ	_variabler2   ÚsqrtÚpiÚ_normalizationr3   Ú_log_normalizationr    r-   r1   r7   r:   r=   r@   rC   rF   rI   rL   rO   rR   r\   rd   rh   ro   Úordersrv   r€   Ú__static_attributes__Ú__classdictcell__Ú__classcell__©r$   Ú__classdict__s   @@r%   r   r      sI  ù‡ € ñ	ñ ¨3¨$°¨Ô5€JÙ!¨Q°¨HÔ5€MÙ¨3¨$°¨Ô5€Já˜t¨V¸JØ'.ô0€Iá! '°)ÀMØ*4ô6€Lá˜c¨*¸gÔF€Há+¨I°|ÓDÐEÐà€IØ�r—w’w˜q §¡�wÓ'Õ'€NØŸš  "§%¡%¥›¨Õ*Ð÷$ð
7˜Rð 7 r÷ 7òTòIòDòAòEòBòBòEòCòFòJòHòòòð #$ Q ÐÔòQ÷Dò Dr'   c                 ól   € \         P                  ! W\        P                  R ,          ,           .^ R7      # )y              ð?rZ   )r   r^   r2   r“   )Úlog_pÚlog_qs   &&r%   Ú	_log_diffrŸ   {   s$   € Ü×Ò˜e¬2¯5©5°­8¥^Ð4¸1Ô=Ð=r'   c                   ó¼  a € ] tR t^t o Rt]! ]) ]3R7      t]! R]RR7      t	]	t
. t^]P                  ! ^]P                  ,          4      ,          t]P                   ! ^]P                  ,          4      ^,          t]P$                  ! R4      t]P$                  ! R4      tR tR tR	 tR
 tR tR tR tR tR tR tR tR t R t!R t"R t#R t$R t%R t&R t'Rt(V t)R# )r!   z¼Standard normal distribution.

The probability density function of the standard normal distribution is:

.. math::

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

r   r   r   r(   r)   c                ó4   € \         P                  ! V 3/ VB  R # r   )r   r-   ©r.   r#   s   &,r%   r-   ÚStandardNormal.__init__’   s   € Ü×'Ò'¨Ñ7°Ô7r'   c                óF   € V P                   V^,          ^,          ,           ) # ©é   )r•   ©r.   r   r#   s   &&,r%   r1   ÚStandardNormal._logpdf_formula•   s   € Ø×(Ñ(¨1¨a­4°­6Õ1Ð2Ð2r'   c                ón   € V P                   \        P                  ! V^,          ) ^,          4      ,          # r¥   )r”   r2   Úexpr§   s   &&,r%   r7   ÚStandardNormal._pdf_formula˜   s%   € Ø×"Ñ"¤R§V¢V¨Q°­T¨E°!­G£_Õ4Ð4r'   c                ó.   € \         P                  ! V4      # r   ©r   Úlog_ndtrr§   s   &&,r%   r:   ÚStandardNormal._logcdf_formula›   s   € Ü×Ò Ó"Ð"r'   c                ó.   € \         P                  ! V4      # r   ©r   Úndtrr§   s   &&,r%   r=   ÚStandardNormal._cdf_formulaž   s   € Ü�|Š|˜A‹Ðr'   c                ó0   € \         P                  ! V) 4      # r   r­   r§   s   &&,r%   r@   ÚStandardNormal._logccdf_formula¡   s   € Ü×Ò  Ó#Ð#r'   c                ó0   € \         P                  ! V) 4      # r   r±   r§   s   &&,r%   rC   ÚStandardNormal._ccdf_formula¤   s   € Ü�|Š|˜Q˜BÓÐr'   c                ó.   € \         P                  ! V4      # r   ©r   Úndtrir§   s   &&,r%   rF   ÚStandardNormal._icdf_formula§   ó   € Ü�}Š}˜QÓÐr'   c                ó.   € \         P                  ! V4      # r   ©r   Ú	ndtri_expr§   s   &&,r%   rI   ÚStandardNormal._ilogcdf_formulaª   ó   € Ü× Ò  Ó#Ð#r'   c                ó0   € \         P                  ! V4      ) # r   r¹   r§   s   &&,r%   rL   ÚStandardNormal._iccdf_formula­   ó   € Ü—’˜aÓ Ð Ð r'   c                ó0   € \         P                  ! V4      ) # r   r¾   r§   s   &&,r%   rO   Ú StandardNormal._ilogccdf_formula°   s   € Ü×!Ò! !Ó$Ð$Ð$r'   c                ót   € ^\         P                  ! ^\         P                  ,          4      ,           ^,          # ©rƒ   )r2   r3   r“   r¢   s   &,r%   rR   ÚStandardNormal._entropy_formula³   s"   € Ø”B—F’F˜1œRŸU™U�7“OÕ# QÕ&Ð&r'   c                ó¶   € \         P                  ! \         P                  ! ^\         P                  ,          4      4      \         P                  ! ^4      ,
          # r¥   )r2   Úlog1pr3   r“   r¢   s   &,r%   r\   Ú"StandardNormal._logentropy_formula¶   s.   € Ü�xŠxœŸš˜q¤§¡�w›Ó(¬2¯6ª6°!«9Õ4Ð4r'   c                ó   € ^ # ©r   r+   r¢   s   &,r%   rd   ÚStandardNormal._median_formula¹   ó   € Ùr'   c                ó   € ^ # rÎ   r+   r¢   s   &,r%   rh   ÚStandardNormal._mode_formula¼   rÐ   r'   c                óB   € ^ ^^^ ^^^^ ^^^^ /pVP                  VR4      # rk   )Úget)r.   rn   r#   Úraw_momentss   &&, r%   ro   Ú"StandardNormal._moment_raw_formula¿   s1   € Ø˜!˜Q  1 a¨¨A¨q°!°Q¸Ð:ˆØ�‰˜u dÓ+Ð+r'   c                ó(   € V P                   ! V3/ VB # r   ©ro   ©r.   rn   r#   s   &&,r%   rv   Ú&StandardNormal._moment_central_formulaÃ   ó   € Ø×'Ò'¨Ñ8°Ñ8Ð8r'   c                ó(   € V P                   ! V3/ VB # r   rØ   rÙ   s   &&,r%   Ú_moment_standardized_formulaÚ+StandardNormal._moment_standardized_formulaÆ   rÛ   r'   c                ó4   € VP                  VR 7      R,          # ©)r{   r+   r|   ©r.   r~   r   r#   s   &&&,r%   r€   ÚStandardNormal._sample_formulaÉ   s   € Ø�z‰z˜zˆzÓ*¨2Õ.Ð.r'   r+   N)éûÿÿÿé   )*r…   r†   r‡   rˆ   r‰   r	   r   rŒ   r   r�   r‘   r�   r2   r’   r“   r”   r3   r•   Úfloat64r   r   r-   r1   r7   r:   r=   r@   rC   rF   rI   rL   rO   rR   r\   rd   rh   ro   rv   rÝ   r€   r—   r˜   ©r›   s   @r%   r!   r!      sé   ø‡ € ññ ¨3¨$°¨Ô5€JÙ˜c¨*¸gÔF€HØ€IØÐØ�r—w’w˜q §¡�wÓ'Õ'€NØŸš  "§%¡%¥›¨Õ*ÐØ	�Š�B‹€BØ�JŠJ�r‹N€Eò8ò3ò5ò#òò$ò ò ò$ò!ò%ò'ò5òòò,ò9ò9÷/ð /r'   r!   c                   ó   a € ] tR t^Ít o Rt]! ]) ]3R7      t]! R]RR7      ;t	t
Rt]P                  ]P                  ! ^4      ,          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R tR tR tRt V t!R# )r   z¶Standard logistic distribution.

The probability density function of the standard logistic distribution is:

.. math::

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

r   r   r   c                ó    € \         P                  ! V4      ) pV^\        P                  ! \         P                  ! V4      4      ,          ,
          # r¥   )r2   rS   r   rË   rª   )r.   r   r#   Úys   &&, r%   r1   ÚLogistic._logpdf_formulaÝ   s2   € Ü�VŠV�A‹YˆJˆØ�1”w—}’}¤R§V¢V¨A£YÓ/Õ/Õ/Ð/r'   c                óX   € R \         P                  ! V^,          4      ,          ^,          # ©r„   )r2   Úcoshr§   s   &&,r%   r7   ÚLogistic._pdf_formulaá   s   € à”R—W’W˜Q �U“^Õ# aÕ'Ð'r'   c                ó.   € \         P                  ! V4      # r   ©r   Ú	log_expitr§   s   &&,r%   r:   ÚLogistic._logcdf_formulaå   rÁ   r'   c                ó.   € \         P                  ! V4      # r   ©r   Úexpitr§   s   &&,r%   r=   ÚLogistic._cdf_formulaè   r¼   r'   c                ó0   € \         P                  ! V) 4      # r   rð   r§   s   &&,r%   r@   ÚLogistic._logccdf_formulaë   s   € Ü× Ò  ! Ó$Ð$r'   c                ó0   € \         P                  ! V) 4      # r   rô   r§   s   &&,r%   rC   ÚLogistic._ccdf_formulaî   s   € Ü�}Š}˜a˜RÓ Ð r'   c                ó.   € \         P                  ! V4      # r   ©r   Úlogitr§   s   &&,r%   rF   ÚLogistic._icdf_formulañ   r¼   r'   c                ó0   € \         P                  ! V4      ) # r   rü   r§   s   &&,r%   rL   ÚLogistic._iccdf_formulaô   rÄ   r'   c                ó   € R # )g       @r+   r¢   s   &,r%   rR   ÚLogistic._entropy_formula÷   s   € Ùr'   c                ó.   € \         P                  ! ^4      # r¥   ©r2   r3   r¢   s   &,r%   r\   ÚLogistic._logentropy_formulaú   s   € Ü�vŠv�a‹yÐr'   c                ó   € ^ # rÎ   r+   r¢   s   &,r%   rd   ÚLogistic._median_formulaý   rÐ   r'   c                ó   € ^ # rÎ   r+   r¢   s   &,r%   rh   ÚLogistic._mode_formula   rÐ   r'   c           	     óú   € \        V4      pV^,          '       d   R# \        P                  V,          \        ^V,          ^,
          \	        \
        P                  ! V4      R,          4      ,          4      ,          # )r¦   r(   r‚   )ru   r2   r“   rS   Úfloatr   Ú	bernoulli)r.   rn   r#   Úns   &&, r%   ro   ÚLogistic._moment_raw_formula  sQ   € Ü�‹JˆØˆq�5Œ5ÙÜ�u‰u�a�xœ#˜q !�t a�x¬5´×1BÒ1BÀ1Ó1EÀbÕ1IÓ+JÕJÓKÕKÐKr'   c                ó(   € V P                   ! V3/ VB # r   rØ   rÙ   s   &&,r%   rv   Ú Logistic._moment_central_formula	  rÛ   r'   c                óX   € V P                   ! V3/ VB V P                  V,          ,          # r   )ro   Ú_scalerÙ   s   &&,r%   rÝ   Ú%Logistic._moment_standardized_formula  s&   € Ø×'Ò'¨Ñ8°Ñ8¸4¿;¹;ÈÕ;MÕMÐMr'   c                ó4   € VP                  VR 7      R,          # rà   )Úlogisticrá   s   &&&,r%   r€   ÚLogistic._sample_formula  s   € Ø�|‰| ˆ|Ó,¨RÕ0Ð0r'   r+   N)i÷ÿÿÿé	   )"r…   r†   r‡   rˆ   r‰   r	   r   rŒ   r   r‘   r�   r�   r2   r“   r’   r  r1   r7   r:   r=   r@   rC   rF   rL   rR   r\   rd   rh   ro   rv   rÝ   r€   r—   r˜   ræ   s   @r%   r   r   Í   s¢   ø‡ € ññ ¨3¨$°¨Ô5€JÙ)¨#°jÈ'ÔRÐR€I�ØÐà�U‰U�R—W’W˜Q“ZÕ€Fò0ò(ò$ò ò%ò!ò ò!òòòòòLò9òN÷1ð 1r'   c                   óÐ  a a€ ] tR tRt oRt]! ^ ]3R7      t]! R]3R7      t]! ]) ]3R7      t	]! R]3R7      t
]! RRR7      t]! R]RR7      t]! R]RR7      t]! RR	]	RR
7      t]! RR]
RR
7      t]! R]RR7      t]P%                  ]4       ]
P%                  ]4       ]P%                  ]]4       ]! ]]4      ]! ]]4      .t]tRRRRRRRR/V 3R lltRR ltR tR tRtVtV ;t# )Ú_LogUniformi  aŠ  Log-uniform distribution.

The probability density function of the log-uniform distribution is:

.. math::

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

If :math:`\log(X)` is a random variable that follows a uniform distribution
between :math:`\log(a)` and :math:`\log(b)`, then :math:`X` is log-uniformly
distributed with shape parameters :math:`a` and :math:`b`.

r   ÚaÚlog_aÚb©r   Ú	inclusiver   z\log(a)r   Úlog_bz\log(b)r   Nc               ó8   <€ \         SV `  ! RR VRVRVRV/VB  R# )r  r  r  r  Nr+   r,   )r.   r  r  r  r  r#   r$   s   &$$$$,€r%   r-   Ú_LogUniform.__init__:  s'   ø€ Ü‰ÒÑF˜1ÐF ÐF¨ÐF°eÐF¸vÔFr'   c           	     ó  € Vf   \         P                  ! V4      MTpVf   \         P                  ! V4      MTpVf   \         P                  ! V4      MTpVf   \         P                  ! V4      MTpVP                  \	        WW4R7      4       V# )N)r  r  r  r  )r2   rª   r3   ÚupdateÚdict)r.   r  r  r  r  r#   s   &&&&&,r%   Ú_process_parametersÚ_LogUniform._process_parameters=  sf   € ØšYŒB�FŠF�5ŒM¨AˆØšYŒB�FŠF�5ŒM¨AˆØ"š]”—’�q”	°ˆØ"š]”—’�q”	°ˆØ�‰”d˜Q¨5Ô>Ô?Øˆr'   c               ó.   € W2,
          V,          R,          # )rƒ   r‚   r+   )r.   r   r  r  r#   s   &&$$,r%   r7   Ú_LogUniform._pdf_formulaH  s   € Ø• Õ! BÕ&Ð&r'   c           	     óø   € V^ 8X  d   V P                   # V P                   W2,
          ,          V,          p\        P                  ! \        P                  ! \	        W,          W,          4      4      4      pWV,          # rÎ   )Ú_oner2   Úrealrª   rŸ   )r.   rn   r  r  r#   Út1Út2s   &&&&,  r%   ro   Ú_LogUniform._moment_raw_formulaN  sQ   € Ø�AŒ:Ø—9‘9ÐØ�Y‰Y˜%�-Õ(¨5Õ0ˆÜ�WŠW”R—V’VœI e¥m°Uµ]ÓCÓDÓEˆØ�wˆr'   r+   ©r  r  ©TT©gü©ñÒMbP?gÍÌÌÌÌÌì?©gš™™™™™ñ?g     @�@)éýÿÿÿgš™™™™™¹¿)çš™™™™™¹?é   )NNNN)r…   r†   r‡   rˆ   r‰   r	   r   Ú	_a_domainÚ	_b_domainÚ_log_a_domainÚ_log_b_domainrŒ   r   Ú_a_paramÚ_b_paramÚ_log_a_paramÚ_log_b_paramr�   Údefine_parametersr   r�   r‘   r-   r%  r7   ro   r—   r˜   r™   rš   s   @@r%   r  r    s,  ù‡ € ññ ¨¨C¨Ô1€IÙ¨¨c¨
Ô3€IÙ!¨c¨T°3¨KÔ8€MÙ!¨W°c¨NÔ;€MÙ¨¸|ÔL€Já˜c¨)¸[ÔI€HÙ˜c¨)¸ZÔH€HÙ! '°*Ø)6À
ôL€Lá! '°*Ø)6ÀôJ€Lá˜c¨*¸jÔI€Hà×Ñ Ô)Ø×#Ñ# LÔ1Ø× Ñ  ¨8Ô4á+¨L¸,ÓGÙ+¨H°hÓ?ðAÐà€IðG˜Dð G Dð G°ð G¸D÷ Gôò'÷ò r'   r  c                   ó’  a a€ ] tR tRt oRt]! ]) ]3R7      t]! R]3R7      t]! RRR7      t	]
! R]RR7      t]
! R]RR7      t]
! R]	RR7      t]P                  ]4       ]	P                  ]]4       ]! ]]4      .t]tRR	RR	/V 3R
 ll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R tR t ^.] n!        R t"Rt#Vt$V ;t%# ) r   iV  z�Uniform distribution.

The probability density function of the uniform distribution is:

.. math::

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

r   r  r  r  r   r   Nc               ó0   <€ \         SV `  ! RR VRV/VB  R# )r  r  Nr+   r,   )r.   r  r  r#   r$   s   &$$,€r%   r-   ÚUniform.__init__p  ó   ø€ Ü‰ÒÑ,˜1Ð, Ð, VÔ,r'   c                óN   € W!,
          pVP                  \        WVR 7      4       V# ))r  r  Úab)r#  r$  ©r.   r  r  rD  r#   s   &&&&,r%   r%  ÚUniform._process_parameterss  s!   € Ø�UˆØ�‰”d˜Q¨Ô+Ô,Øˆr'   c               ó    € \         P                  ! \         P                  ! V4      \         P                  \         P                  ! V4      ) 4      # r   )r2   ÚwhereÚisnanÚnanr3   ©r.   r   rD  r#   s   &&$,r%   r1   ÚUniform._logpdf_formulax  s+   € Ü�xŠxœŸš ›¤R§V¡V¬b¯fªf°R«j¨[Ó9Ð9r'   c               ó„   € \         P                  ! \         P                  ! V4      \         P                  ^V,          4      # rÈ   )r2   rH  rI  rJ  rK  s   &&$,r%   r7   ÚUniform._pdf_formula{  s%   € Ü�xŠxœŸš ›¤R§V¡V¨Q¨r­TÓ2Ð2r'   c               óì   € \         P                  ! R R7      ;_uu_ 4        \         P                  ! W,
          4      \         P                  ! V4      ,
          uuRRR4       #   + '       g   i     R# ; i©rW   rX   N©r2   r]   r3   ©r.   r   r  rD  r#   s   &&$$,r%   r:   ÚUniform._logcdf_formula~  ó:   € Ü�[Š[ ×)Ö)Ü—6’6˜!�%“=¤2§6¢6¨"£:Õ-÷ *×)×)Ó)úó    7A"Á"A3	c               ó    € W,
          V,          # r   r+   rR  s   &&$$,r%   r=   ÚUniform._cdf_formula‚  ó   € Ø•˜�|Ðr'   c               óì   € \         P                  ! R R7      ;_uu_ 4        \         P                  ! W!,
          4      \         P                  ! V4      ,
          uuRRR4       #   + '       g   i     R# ; irP  rQ  ©r.   r   r  rD  r#   s   &&$$,r%   r@   ÚUniform._logccdf_formula…  rT  rU  c               ó    € W!,
          V,          # r   r+   rZ  s   &&$$,r%   rC   ÚUniform._ccdf_formula‰  rX  r'   c               ó    € W#V,          ,           # r   r+   )r.   Úpr  rD  r#   s   &&$$,r%   rF   ÚUniform._icdf_formulaŒ  ó   € Ø�a•4�xˆr'   c               ó    € W#V,          ,
          # r   r+   )r.   r_  r  rD  r#   s   &&$$,r%   rL   ÚUniform._iccdf_formula�  ra  r'   c               ó.   € \         P                  ! V4      # r   r  )r.   rD  r#   s   &$,r%   rR   ÚUniform._entropy_formula’  s   € Ü�vŠv�b‹zÐr'   c               ó"   € VR V,          ,           # rì   r+   rE  s   &$$$,r%   rh   ÚUniform._mode_formula•  ó   € Ø�3�r•6�zÐr'   c               ó"   € VR V,          ,           # rì   r+   rE  s   &$$$,r%   rd   ÚUniform._median_formula˜  rh  r'   c                óX   € V^,           pW6,          W&,          ,
          Wd,          ,          # rÈ   r+   )r.   rn   r  r  rD  r#   Únp1s   &&&&&, r%   ro   ÚUniform._moment_raw_formula›  s    € Ø�a�iˆØ•˜�• C¥HÕ-Ð-r'   c                ó4   € V^8X  d   V^,          ^,          # R# )r¦   Nr+   )r.   rn   rD  r#   s   &&&,r%   rv   ÚUniform._moment_central_formulaŸ  s   € Ø  Aœ:ˆr�1�u�R�xÐ/¨4Ð/r'   c                óž   €  VP                  W4VR 7      R,          #   \         d&    TP                  ^ ^TR 7      T,          T,           u # i ; irà   )ÚuniformÚOverflowError)r.   r~   r   r  r  rD  r#   s   &&&&&&,r%   r€   ÚUniform._sample_formula¤  sM   € ð	=Ø—;‘;˜q¨*�;Ó5°bÕ9Ð9øÜô 	=Ø—;‘;˜q !¨*�;Ó5°bÕ8¸1Õ<Ò<ð	=ús   ‚ œ-AÁAr+   r/  r0  r1  r2  )NNN)&r…   r†   r‡   rˆ   r‰   r	   r   r6  r7  rŒ   r   r:  r;  r�   r>  r   r�   r‘   r-   r%  r1   r7   r:   r=   r@   rC   rF   rL   rR   rh   rd   ro   rv   r–   r€   r—   r˜   r™   rš   s   @@r%   r   r   V  s  ù‡ € ñ	ñ ¨#¨¨s¨Ô4€IÙ¨¨c¨
Ô3€IÙ¨¸|ÔL€Já˜c¨)¸[ÔI€HÙ˜c¨)¸ZÔH€HÙ˜c¨*¸jÔI€Hà×Ñ Ô)Ø× Ñ  ¨8Ô4á+¨H°hÓ?Ð@ÐØ€Ið-˜Dð - D÷ -ôò
:ò3ò.òò.òòòòòòò.ò0ð '( SÐÔ"÷=ò =r'   c                   ó–   a € ] tR tRt o ]! ^ ]3R7      t]! ^ ]3R
R7      t]! R]RR7      t	]! R]RR7      t
]! ]	4      .t]
tR tRtV tR	# )Ú_Gammai«  r   r  r  r   r   c               óŽ   € W^,
          ,          \         P                  ! V) 4      ,          \        P                  ! V4      ,          # rÈ   )r2   rª   r   Úgamma)r.   r   r  r#   s   &&$,r%   r7   Ú_Gamma._pdf_formula¶  s+   € Ø˜•U�|œbŸfšf a R›jÕ(¬7¯=ª=¸Ó+;Õ;Ð;r'   r+   N©FF)r4  é
   )r…   r†   r‡   rˆ   r	   r   r6  rŒ   r   r:  r�   r   r�   r‘   r7   r—   r˜   ræ   s   @r%   ru  ru  «  s\   ø‡ € á¨¨C¨Ô1€IÙ¨!¨S¨¸^ÔL€Já˜c¨)¸YÔG€HÙ˜c¨*¸iÔH€Há+¨HÓ5Ð6ÐØ€I÷<ð <r'   ru  c                   ó6  a a€ ] tR tRt oRt]! ^ ]3RR7      t]! RRR7      t	]! RRR7      t
]! R]RR7      t]! R]	RR7      t]! R]
RR7      t]! ]]4      .t]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^^.]n        R t. RO]n        RtVt V ;t!# )r   iº  zÊBinomial distribution with prescribed success probability and number of trials

The probability density function of the binomial distribution is:

.. math::

    f(x) = {n \choose x} p^x (1 - p)^{n-x}

r  r  r   r_  r   c               ó0   <€ \         SV `  ! RR VRV/VB  R# )r  r_  Nr+   r,   )r.   r  r_  r#   r$   s   &$$,€r%   r-   ÚBinomial.__init__Ï  rB  r'   c               ó0   € \         P                  ! WV4      # r   )ÚscuÚ
_binom_pmf©r.   r   r  r_  r#   s   &&$$,r%   Ú_pmf_formulaÚBinomial._pmf_formulaÒ  ó   € Ü�~Š~˜a AÓ&Ð&r'   c               óP  € \         P                  ! V^,           4      \         P                  ! V^,           4      \         P                  ! W!,
          ^,           4      ,           ,
          pV\         P                  ! W4      ,           \         P                  ! W!,
          V) 4      ,           # rÈ   )r   ÚgammalnÚxlogyÚxlog1py)r.   r   r  r_  r#   Úcombilns   &&$$, r%   Ú_logpmf_formulaÚBinomial._logpmf_formulaÕ  si   € ô
 �OŠO˜A˜a�CÓ ¤G§O¢O°A°aµCÓ$8¼7¿?º?È1Í3ÈqÍ5Ó;QÕ$QÕRð 	ð œŸš qÓ,Õ,¬w¯ª¸q½sÀQÀBÓ/GÕGÐGr'   c               ó0   € \         P                  ! WV4      # r   )r  Ú
_binom_cdfr�  s   &&$$,r%   r=   ÚBinomial._cdf_formulaÞ  r„  r'   c               óf   € V P                  R W#R7      p\        P                  ! W8  WV3R R 4      # )r„   ©r  r_  c                  óR   € \         P                  ! \        P                  ! V !  4      # r   )r2   r3   r  r�  ©Úargss   *r%   Ú<lambda>Ú*Binomial._logcdf_formula.<locals>.<lambda>æ  s   € œ"Ÿ&š&¤§¢°Ñ!6Ô7r'   c                  óT   € \         P                  ! \        P                  ! V !  ) 4      # r   )r2   rË   r  Ú	_binom_sfr’  s   *r%   r”  r•  ç  s   € œ"Ÿ(š(¤C§M¢M°4Ñ$8Ð#8Ô9r'   ©rF   ÚxpxÚapply_where©r.   r   r  r_  r#   Úmedians   &&$$, r%   r:   ÚBinomial._logcdf_formulaá  s:   € ð ×#Ñ# C¨1Ð#Ó2ˆÜ�Š˜q™z¨A°!¨9Ù7Ù9ó
ð 	
r'   c               ó0   € \         P                  ! WV4      # r   )r  r—  r�  s   &&$$,r%   rC   ÚBinomial._ccdf_formulaê  s   € Ü�}Š}˜Q 1Ó%Ð%r'   c               óf   € V P                  R W#R7      p\        P                  ! W8  WV3R R 4      # )r„   r�  c                  óT   € \         P                  ! \        P                  ! V !  ) 4      # r   )r2   rË   r  r�  r’  s   *r%   r”  Ú+Binomial._logccdf_formula.<locals>.<lambda>ð  s   € œ"Ÿ(š(¤C§N¢N°DÑ$9Ð#9Ô:r'   c                  óR   € \         P                  ! \        P                  ! V !  4      # r   )r2   r3   r  r—  r’  s   *r%   r”  r¢  ñ  s   € œ"Ÿ&š&¤§¢°Ñ!5Ô6r'   r˜  r›  s   &&$$, r%   r@   ÚBinomial._logccdf_formulaí  s8   € Ø×#Ñ# C¨1Ð#Ó2ˆÜ�Š˜q™z¨A°!¨9Ù:Ù6ó
ð 	
r'   c               ó0   € \         P                  ! WV4      # r   )r  Ú
_binom_ppfr�  s   &&$$,r%   rF   ÚBinomial._icdf_formulaô  r„  r'   c               ó0   € \         P                  ! WV4      # r   )r  Ú
_binom_isfr�  s   &&$$,r%   rL   ÚBinomial._iccdf_formula÷  r„  r'   c               ó    € \         P                  ! V^,           V,          4      p\         P                  ! V^8H  V^,
          V4      pVR,          # )rƒ   r+   )r2   ÚfloorrH  )r.   r  r_  r#   Úmodes   &$$, r%   rh   ÚBinomial._mode_formulaú  s;   € ä�xŠx˜˜1�˜a�Ó ˆÜ�xŠx˜˜Q™  q¥¨$Ó/ˆØ�B�xˆr'   c               óx   € V^8X  d	   W#,          # V^8X  d$   W#,          ^V,
          W#,          ,           ,          # R# ©rƒ   Nr+   ©r.   rn   r  r_  r#   s   &&$$,r%   ro   ÚBinomial._moment_raw_formula   s1   € à�AŒ:Ø•3ˆJØ�AŒ:Ø•3˜˜A� ¥�Õ$Ð$Ùr'   c               óz  € V^8X  d   \         P                  ! V4      # V^8X  d   W#,          ^V,
          ,          # V^8X  d,   W#,          ^V,
          ,          ^^V,          ,
          ,          # V^8X  dH   W#,          ^V,
          ,          ^^V,          ^,
          V,          ^V,
          ,          ,           ,          # R# r°  )r2   rs   r±  s   &&$$,r%   rv   Ú Binomial._moment_central_formula	  sŒ   € à�AŒ:Ü—=’= Ó#Ð#Ø�AŒ:Ø•3˜˜A�•;ÐØ�AŒ:Ø•3˜˜A�•;  A a¥C¥Õ(Ð(Ø�AŒ:Ø•3˜˜A�•;  Q q¥S¨1¥W¨a¥K°°QµÕ$7Õ 7Õ8Ð8Ùr'   r+   ry  )r   rƒ   )r   r  r0  )rz  é   )g      Ð?g      è?)r   rz  )rƒ   r¦   r5  é   )"r…   r†   r‡   rˆ   r‰   r
   r   Ú	_n_domainr	   Ú	_p_domainrŒ   r   Ú_n_paramÚ_p_paramr�   r   r�   r‘   r-   r‚  rŠ  r=   r:   rC   r@   rF   rL   rh   ro   r–   rv   r—   r˜   r™   rš   s   @@r%   r   r   º  sÍ   ù‡ € ññ !¨A¨s¨8¸~ÔN€IÙ¨¸.ÔI€IÙ!¨HÀÔM€Já˜c¨)¸XÔF€HÙ˜c¨)¸\ÔJ€HÙ˜c¨*¸gÔF€Há+¨H°hÓ?Ð@ÐØ€Iõ-ò'òHò'ò
ò&ò
ò'ò'òòð #$ Q ÐÔò
ò &2Ð×"Ô"r'   )r   r   r   r   )#ÚsysÚnumpyr2   r   Ú
scipy._libr   r™  Úscipyr   Úscipy.specialr   r  Ú(scipy.stats._distribution_infrastructurer   r   r	   r
   r   r   r   Ú__all__r   rŸ   r!   r   r  r   ru  r   Úmodulesr…   Ú__dict__Ú_moduleÚ	dist_namer‰   r+   r'   r%   Ú<module>rÆ     sÕ   ðÛ 
ã Ý å -Ý Ý (÷6÷ 6ñ 6ò 8€ôhDÐ#ô hDòV>ôK/�Vô K/ô\C1Ð%ô C1ôN?Ð(ô ?ôDR=Ð$ô R=ôj<Ð#ô <ôZ2Ð#ô Z2ð@ �+‰+�hÕ
×
(Ñ
(€Û€IÙ!.¨w°yÕ/AÓ!B€GˆIÕÖó r'   