ó
    EñiëI  ã                   óz  • S SK r S SKrS SKJr  S SKJr  S SKJr  S SK	J
r  S SKJrJrJrJrJrJrJr  / SQr " S S	\5      rS
 r " S S\5      r " S S\5      r " S S\5      r " S S\5      r " S S\5      r " S S\5      r\ R:                  \   R>                  r \ H  r!\" \ \!   5      \ \!   l"        M     g)é    N)Úinf)Úarray_api_extra)Úspecial)Ú_ufuncs)ÚContinuousDistributionÚDiscreteDistributionÚ_RealIntervalÚ_IntegerIntervalÚ_RealParameterÚ_ParameterizationÚ_combine_docs)ÚNormalÚLogisticÚUniformÚBinomialc                   óÆ  ^ • \ rS rSrSr\" \* \4S9r\" S\4S9r\" \* \4S9r	\
" SS\SS9r\
" S	S
\SS9r\
" S\	SS9r\" \\5      /r\rS\R$                  " S\R&                  -  5      -  r\R*                  " S\R&                  -  5      S-  rS'U 4S jjrSSS.U 4S jjrS rS rS rS rS rS rS rS r S r!S r"S r#S  r$S! r%S" r&S# r'SS/\'l(        S$ r)S% r*S&r+U =r,$ )(r   é   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	endpointsr   Úmuz\mu)éÿÿÿÿé   ©ÚsymbolÚdomainÚtypicalÚsigmaz\sigma)ç      à?g      ø?Úx©r   r   r   é   c                 óT   >• Uc  Uc  [         TU ]  [        5      $ [         TU ]  U 5      $ ©N)ÚsuperÚ__new__ÚStandardNormal)Úclsr   r   ÚkwargsÚ	__class__s       €Ú[/home/mande/repo/quber/.venv/lib/python3.13/site-packages/scipy/stats/_new_distributions.pyr%   ÚNormal.__new__.   s*   ø€ Ø‰:˜%™-Ü‘7‘?¤>Ó2Ð2Ü‰w‰˜sÓ#Ð#ó    ç        ç      ð?©r   r   c                ó*   >• [         TU ]  " SXS.UD6  g )Nr/   © ©r$   Ú__init__)Úselfr   r   r(   r)   s       €r*   r3   ÚNormal.__init__3   s   ø€ Ü‰ÒÐ6˜BÑ6¨vÓ6r,   c                óf   • [         R                  XU-
  U-  5      [        R                  " U5      -
  $ r#   )r&   Ú_logpdf_formulaÚnpÚlog©r4   r   r   r   r(   s        r*   r7   ÚNormal._logpdf_formula6   s(   € Ü×-Ñ-¨d¸±V¸U±NÓCÄbÇfÂfÈUÃmÑSÐSr,   c                ó>   • [         R                  XU-
  U-  5      U-  $ r#   )r&   Ú_pdf_formular:   s        r*   r=   ÚNormal._pdf_formula9   s    € Ü×*Ñ*¨4°b±&¸%±Ó@À5ÑHÐHr,   c                ó8   • [         R                  XU-
  U-  5      $ r#   )r&   Ú_logcdf_formular:   s        r*   r@   ÚNormal._logcdf_formula<   s   € Ü×-Ñ-¨d¸±V¸U±NÓCÐCr,   c                ó8   • [         R                  XU-
  U-  5      $ r#   )r&   Ú_cdf_formular:   s        r*   rC   ÚNormal._cdf_formula?   s   € Ü×*Ñ*¨4°b±&¸%±Ó@Ð@r,   c                ó8   • [         R                  XU-
  U-  5      $ r#   )r&   Ú_logccdf_formular:   s        r*   rF   ÚNormal._logccdf_formulaB   s   € Ü×.Ñ.¨t¸"±f¸e±^ÓDÐDr,   c                ó8   • [         R                  XU-
  U-  5      $ r#   )r&   Ú_ccdf_formular:   s        r*   rI   ÚNormal._ccdf_formulaE   s   € Ü×+Ñ+¨D°r±6¸5±.ÓAÐAr,   c                ó8   • [         R                  X5      U-  U-   $ r#   )r&   Ú_icdf_formular:   s        r*   rL   ÚNormal._icdf_formulaH   s   € Ü×+Ñ+¨DÓ4°uÑ<¸rÑAÐAr,   c                ó8   • [         R                  X5      U-  U-   $ r#   )r&   Ú_ilogcdf_formular:   s        r*   rO   ÚNormal._ilogcdf_formulaK   s   € Ü×.Ñ.¨tÓ7¸%Ñ?À"ÑDÐDr,   c                ó8   • [         R                  X5      U-  U-   $ r#   )r&   Ú_iccdf_formular:   s        r*   rR   ÚNormal._iccdf_formulaN   s   € Ü×,Ñ,¨TÓ5¸Ñ=ÀÑBÐBr,   c                ó8   • [         R                  X5      U-  U-   $ r#   )r&   Ú_ilogccdf_formular:   s        r*   rU   ÚNormal._ilogccdf_formulaQ   s   € Ü×/Ñ/°Ó8¸5Ñ@À2ÑEÐEr,   c                ól   • [         R                  U 5      [        R                  " [	        U5      5      -   $ r#   )r&   Ú_entropy_formular8   r9   Úabs©r4   r   r   r(   s       r*   rX   ÚNormal._entropy_formulaT   s%   € Ü×.Ñ.¨tÓ4´r·v²v¼cÀ%»jÓ7IÑIÐIr,   c                óH  • [         R                  U 5      n[        R                  " SS9   [        R                  " [        R                  " [        U5      5      S-   5      nS S S 5        [        R                  " [        R                  " UW5      SS9$ ! , (       d  f       N8= f)NÚignore©Údividey                r   ©Úaxis)	r&   Ú_logentropy_formular8   Úerrstater9   rY   r   Ú	logsumexpÚbroadcast_arrays)r4   r   r   r(   ÚlH0Úllss         r*   rb   ÚNormal._logentropy_formulaW   sp   € Ü×0Ñ0°Ó6ˆÜ�[Š[ Ó)ô —&’&œŸš¤ E£
Ó+¨BÑ.Ó/ˆC÷ *ô × Ò ¤×!4Ò!4°S¸#Ó!>ÀQÑGÐG÷	 *Õ)ús   ª7BÂ
B!c                ó   • U$ r#   r1   rZ   s       r*   Ú_median_formulaÚNormal._median_formula_   ó   € Øˆ	r,   c                ó   • U$ r#   r1   rZ   s       r*   Ú_mode_formulaÚNormal._mode_formulab   rl   r,   c                óL   • US:X  a  [         R                  " U5      $ US:X  a  U$ g )Nr   r   )r8   Ú	ones_like©r4   Úorderr   r   r(   s        r*   Ú_moment_raw_formulaÚNormal._moment_raw_formulae   s'   € Ø�A‹:Ü—<’< Ó#Ð#Ø�a‹ZØˆIàr,   c                óÆ   • US:X  a  [         R                  " U5      $ US-  (       a  [         R                  " U5      $ X1-  [        R                  " [        U5      S-
  SS9-  $ )Nr   r!   r   T)Úexact)r8   rq   Ú
zeros_liker   Ú
factorial2Úintrr   s        r*   Ú_moment_central_formulaÚNormal._moment_central_formulan   sR   € Ø�A‹:Ü—<’< Ó#Ð#Ø�Q�YÜ—=’= Ó$Ð$ð ‘<¤'×"4Ò"4´S¸³ZÀ!±^È4Ñ"PÑPÐPr,   c                ó(   • UR                  X4US9S   $ )N)ÚlocÚscaleÚsizer1   ©Únormal)r4   Ú
full_shapeÚrngr   r   r(   s         r*   Ú_sample_formulaÚNormal._sample_formulaw   s   € Ø�z‰z˜b°JˆzÐ?ÀÑCÐCr,   r1   )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	_variabler8   ÚsqrtÚpiÚ_normalizationr9   Ú_log_normalizationr%   r3   r7   r=   r@   rC   rF   rI   rL   rO   rR   rU   rX   rb   rj   rn   rt   Úordersr{   r…   Ú__static_attributes__Ú__classcell__©r)   s   @r*   r   r      sE  ø† ñ	ñ ¨3¨$°¨Ñ5€JÙ!¨Q°¨HÑ5€MÙ¨3¨$°¨Ñ5€Já˜t¨V¸JØ'.ñ0€Iá! '°)ÀMØ*4ñ6€Lá˜c¨*¸gÑF€Há+¨I°|ÓDÐEÐà€IØ�r—w’w˜q §¡™wÓ'Ñ'€NØŸš  "§%¡%¡›¨Ñ*Ð÷$ð
   r÷ 7ð 7òTòIòDòAòEòBòBòEòCòFòJòHòòòð #$ Q ÐÔòQ÷Dð Dr,   r   c                 óV   • [         R                  " X[        R                  S-  -   /SS9$ )Ny              ð?r   r`   )r   rd   r8   r•   )Úlog_pÚlog_qs     r*   Ú	_log_diffrŸ   {   s$   € Ü×Ò˜e¬2¯5©5°©8¡^Ð4¸1Ñ=Ð=r,   c                   ó„  • \ rS rSrSr\" \* \4S9r\" S\SS9r	\	r
/ rS\R                  " S\R                  -  5      -  r\R                   " S\R                  -  5      S-  r\R$                  " S	5      r\R$                  " S
5      rS rS rS rS rS rS rS rS rS rS rS rS r S r!S r"S r#S r$S r%S r&S r'Sr(g) r&   é   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   )éûÿÿÿé   r    r   r!   r-   r.   c                 ó2   • [         R                  " U 40 UD6  g r#   )r   r3   ©r4   r(   s     r*   r3   ÚStandardNormal.__init__’   s   € Ü×'Ò'¨Ñ7°Ó7r,   c                 ó.   • U R                   US-  S-  -   * $ ©Nr!   )r—   ©r4   r   r(   s      r*   r7   ÚStandardNormal._logpdf_formula•   s   € Ø×(Ñ(¨1¨a©4°©6Ñ1Ð2Ð2r,   c                 óV   • U R                   [        R                  " US-  * S-  5      -  $ r¨   )r–   r8   Úexpr©   s      r*   r=   ÚStandardNormal._pdf_formula˜   s%   € Ø×"Ñ"¤R§V¢V¨Q°©T¨E°!©G£_Ñ4Ð4r,   c                 ó.   • [         R                  " U5      $ r#   ©r   Úlog_ndtrr©   s      r*   r@   ÚStandardNormal._logcdf_formula›   s   € Ü×Ò Ó"Ð"r,   c                 ó.   • [         R                  " U5      $ r#   ©r   Úndtrr©   s      r*   rC   ÚStandardNormal._cdf_formulaž   s   € Ü�|Š|˜A‹Ðr,   c                 ó0   • [         R                  " U* 5      $ r#   r¯   r©   s      r*   rF   ÚStandardNormal._logccdf_formula¡   s   € Ü×Ò  Ó#Ð#r,   c                 ó0   • [         R                  " U* 5      $ r#   r³   r©   s      r*   rI   ÚStandardNormal._ccdf_formula¤   s   € Ü�|Š|˜Q˜BÓÐr,   c                 ó.   • [         R                  " U5      $ r#   ©r   Úndtrir©   s      r*   rL   ÚStandardNormal._icdf_formula§   ó   € Ü�}Š}˜QÓÐr,   c                 ó.   • [         R                  " U5      $ r#   ©r   Ú	ndtri_expr©   s      r*   rO   ÚStandardNormal._ilogcdf_formulaª   ó   € Ü× Ò  Ó#Ð#r,   c                 ó0   • [         R                  " U5      * $ r#   r»   r©   s      r*   rR   ÚStandardNormal._iccdf_formula­   ó   € Ü—’˜aÓ Ð Ð r,   c                 ó0   • [         R                  " U5      * $ r#   rÀ   r©   s      r*   rU   Ú StandardNormal._ilogccdf_formula°   s   € Ü×!Ò! !Ó$Ð$Ð$r,   c                 ó\   • S[         R                  " S[         R                  -  5      -   S-  $ ©Nr   r!   )r8   r9   r•   r¥   s     r*   rX   ÚStandardNormal._entropy_formula³   s"   € Ø”B—F’F˜1œRŸU™U™7“OÑ# QÑ&Ð&r,   c                 ó¦   • [         R                  " [         R                  " S[         R                  -  5      5      [         R                  " S5      -
  $ r¨   )r8   Úlog1pr9   r•   r¥   s     r*   rb   Ú"StandardNormal._logentropy_formula¶   s.   € Ü�xŠxœŸš˜q¤§¡™w›Ó(¬2¯6ª6°!«9Ñ4Ð4r,   c                 ó   • g©Nr   r1   r¥   s     r*   rj   ÚStandardNormal._median_formula¹   ó   € Ør,   c                 ó   • grÐ   r1   r¥   s     r*   rn   ÚStandardNormal._mode_formula¼   rÒ   r,   c                 ó8   • SSSSSSS.nUR                  US 5      $ )Nr   r   é   )r   r   r!   rÖ   é   r£   )Úget)r4   rs   r(   Úraw_momentss       r*   rt   Ú"StandardNormal._moment_raw_formula¿   s%   € Ø  a¨A°!¸Ñ:ˆØ�‰˜u dÓ+Ð+r,   c                 ó(   • U R                   " U40 UD6$ r#   ©rt   ©r4   rs   r(   s      r*   r{   Ú&StandardNormal._moment_central_formulaÃ   ó   € Ø×'Ò'¨Ñ8°Ñ8Ð8r,   c                 ó(   • U R                   " U40 UD6$ r#   rÜ   rÝ   s      r*   Ú_moment_standardized_formulaÚ+StandardNormal._moment_standardized_formulaÆ   rß   r,   c                 ó&   • UR                  US9S   $ ©N©r€   r1   r�   ©r4   rƒ   r„   r(   s       r*   r…   ÚStandardNormal._sample_formulaÉ   s   € Ø�z‰z˜zˆzÐ*¨2Ñ.Ð.r,   r1   N))r‡   rˆ   r‰   rŠ   r‹   r	   r   rŽ   r   r‘   r“   r’   r8   r”   r•   r–   r9   r—   Úfloat64r   r   r3   r7   r=   r@   rC   rF   rI   rL   rO   rR   rU   rX   rb   rj   rn   rt   r{   rá   r…   r™   r1   r,   r*   r&   r&      sá   † ññ ¨3¨$°¨Ñ5€JÙ˜c¨*¸gÑF€HØ€IØÐØ�r—w’w˜q §¡™wÓ'Ñ'€NØŸš  "§%¡%¡›¨Ñ*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9õ/r,   r&   c                   óà   • \ rS rSrSr\" \* \4S9r\" S\SS9=r	r
Sr\R                  \R                  " S5      -  rS	 rS
 rS rS rS rS rS rS rS rS rS rS rS rS rS rS rSr g)r   éÍ   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   )i÷ÿÿÿé	   r    r1   rÖ   c                 ó�   • [         R                  " U5      * nUS[        R                  " [         R                  " U5      5      -  -
  $ r¨   )r8   rY   r   rÍ   r¬   )r4   r   r(   Úys       r*   r7   ÚLogistic._logpdf_formulaÝ   s2   € Ü�VŠV�A‹YˆJˆØ�1”w—}’}¤R§V¢V¨A£YÓ/Ñ/Ñ/Ð/r,   c                 ó@   • S[         R                  " US-  5      -  S-  $ )Nr   r!   )r8   Úcoshr©   s      r*   r=   ÚLogistic._pdf_formulaá   s   € à”R—W’W˜Q ™U“^Ñ# aÑ'Ð'r,   c                 ó.   • [         R                  " U5      $ r#   ©r   Ú	log_expitr©   s      r*   r@   ÚLogistic._logcdf_formulaå   rÃ   r,   c                 ó.   • [         R                  " U5      $ r#   ©r   Úexpitr©   s      r*   rC   ÚLogistic._cdf_formulaè   r¾   r,   c                 ó0   • [         R                  " U* 5      $ r#   ró   r©   s      r*   rF   ÚLogistic._logccdf_formulaë   s   € Ü× Ò  ! Ó$Ð$r,   c                 ó0   • [         R                  " U* 5      $ r#   r÷   r©   s      r*   rI   ÚLogistic._ccdf_formulaî   s   € Ü�}Š}˜a˜RÓ Ð r,   c                 ó.   • [         R                  " U5      $ r#   ©r   Úlogitr©   s      r*   rL   ÚLogistic._icdf_formulañ   r¾   r,   c                 ó0   • [         R                  " U5      * $ r#   rÿ   r©   s      r*   rR   ÚLogistic._iccdf_formulaô   rÆ   r,   c                 ó   • g)Ng       @r1   r¥   s     r*   rX   ÚLogistic._entropy_formula÷   s   € Ør,   c                 ó.   • [         R                  " S5      $ r¨   ©r8   r9   r¥   s     r*   rb   ÚLogistic._logentropy_formulaú   s   € Ü�vŠv�a‹yÐr,   c                 ó   • grÐ   r1   r¥   s     r*   rj   ÚLogistic._median_formulaý   rÒ   r,   c                 ó   • grÐ   r1   r¥   s     r*   rn   ÚLogistic._mode_formula   rÒ   r,   c           	      ó¾   • [        U5      nUS-  (       a  g[        R                  U-  [        SU-  S-
  [	        [
        R                  " U5      S   5      -  5      -  $ )Nr!   r-   r   )rz   r8   r•   rY   Úfloatr   Ú	bernoulli)r4   rs   r(   Úns       r*   rt   ÚLogistic._moment_raw_formula  sO   € Ü�‹JˆØˆq�5ØÜ�u‰u�a‰xœ#˜q !™t a™x¬5´×1BÒ1BÀ1Ó1EÀbÑ1IÓ+JÑJÓKÑKÐKr,   c                 ó(   • U R                   " U40 UD6$ r#   rÜ   rÝ   s      r*   r{   Ú Logistic._moment_central_formula	  rß   r,   c                 óH   • U R                   " U40 UD6U R                  U-  -  $ r#   )rt   Ú_scalerÝ   s      r*   rá   Ú%Logistic._moment_standardized_formula  s&   € Ø×'Ò'¨Ñ8°Ñ8¸4¿;¹;ÈÑ;MÑMÐMr,   c                 ó&   • UR                  US9S   $ rä   )Úlogisticræ   s       r*   r…   ÚLogistic._sample_formula  s   € Ø�|‰| ˆ|Ð,¨RÑ0Ð0r,   N)!r‡   rˆ   r‰   rŠ   r‹   r	   r   rŽ   r   r“   r‘   r’   r8   r•   r”   r  r7   r=   r@   rC   rF   rI   rL   rR   rX   rb   rj   rn   rt   r{   rá   r…   r™   r1   r,   r*   r   r   Í   sš   † ññ ¨3¨$°¨Ñ5€JÙ)¨#°jÈ'ÑRÐR€I�ØÐà�U‰U�R—W’W˜Q“ZÑ€Fò0ò(ò$ò ò%ò!ò ò!òòòòòLò9òNõ1r,   r   c                   ó„  ^ • \ rS rSrSr\" S\4S9r\" S\4S9r\" \* \4S9r	\" S\4S9r
\" SSS	9r\" S\S
S9r\" S\SS9r\" SS\	SS9r\" SS\
SS9r\" S\SS9r\R%                  \5        \
R%                  \5        \R%                  \\5        \" \\5      \" \\5      /r\rSSSSS.U 4S jjrSS jrS rS rSrU =r$ )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   r   ÚaÚlog_a©r  Úb©TT©r   Ú	inclusive©gü©ñÒMbP?gÍÌÌÌÌÌì?r    r  ©gš™™™™™ñ?g     @�@z\log(a))éýÿÿÿgš™™™™™¹¿r   Úlog_bz\log(b))çš™™™™™¹?rÖ   r   N©r  r  r  r&  c                ó,   >• [         TU ]  " SXX4S.UD6  g )Nr(  r1   r2   )r4   r  r  r  r&  r(   r)   s         €r*   r3   Ú_LogUniform.__init__:  s   ø€ Ü‰ÒÐF˜1¨ÑF¸vÓFr,   c           	      ó  • Uc  [         R                  " U5      OUnUc  [         R                  " U5      OUnUc  [         R                  " U5      OUnUc  [         R                  " U5      OUnUR                  [	        XX4S95        U$ )Nr(  )r8   r¬   r9   ÚupdateÚdict)r4   r  r  r  r&  r(   s         r*   Ú_process_parametersÚ_LogUniform._process_parameters=  sf   € Ø™YŒB�FŠF�5ŒM¨AˆØ™YŒB�FŠF�5ŒM¨AˆØ"™]”—’�q”	°ˆØ"™]”—’�q”	°ˆØ�‰”d˜Q¨5Ñ>Ô?Øˆr,   c                ó   • X2-
  U-  S-  $ )Nr   r1   )r4   r   r  r&  r(   s        r*   r=   Ú_LogUniform._pdf_formulaH  s   € Ø‘ Ñ! BÑ&Ð&r,   c           	      óÆ   • US:X  a  U R                   $ U R                   X2-
  -  U-  n[        R                  " [        R                  " [	        X-  X-  5      5      5      nXV-  $ rÐ   )Ú_oner8   Úrealr¬   rŸ   )r4   rs   r  r&  r(   Út1Út2s          r*   rt   Ú_LogUniform._moment_raw_formulaN  sQ   € Ø�A‹:Ø—9‘9ÐØ�Y‰Y˜%™-Ñ(¨5Ñ0ˆÜ�WŠW”R—V’VœI e¡m°U±]ÓCÓDÓEˆØ‰wˆr,   r1   )NNNN)r‡   rˆ   r‰   rŠ   r‹   r	   r   Ú	_a_domainÚ	_b_domainÚ_log_a_domainÚ_log_b_domainrŽ   r   Ú_a_paramÚ_b_paramÚ_log_a_paramÚ_log_b_paramr‘   Údefine_parametersr   r’   r“   r3   r.  r=   rt   r™   rš   r›   s   @r*   r  r    s  ø† ññ ¨¨C¨Ñ1€IÙ¨¨c¨
Ñ3€IÙ!¨c¨T°3¨KÑ8€MÙ!¨W°c¨NÑ;€MÙ¨¸|ÑL€Já˜c¨)¸[ÑI€HÙ˜c¨)¸ZÑH€HÙ! '°*Ø)6À
ñL€Lá! '°*Ø)6ÀñJ€Lá˜c¨*¸jÑI€Hà×Ñ Ô)Ø×#Ñ# LÔ1Ø× Ñ  ¨8Ô4á+¨L¸,ÓGÙ+¨H°hÓ?ðAÐà€Ià  D°¸D÷ Gð Gôò'÷ð r,   r  c                   ób  ^ • \ rS rSrSr\" \* \4S9r\" S\4S9r\" SSS9r	\
" S\SS	9r\
" S
\SS	9r\
" S\	SS	9r\R                  \5        \	R                  \\5        \" \\5      /r\rSSS.U 4S jjrS S jrS rS rS rS rS rS rS rS rS rS rS rS rS r S/\ l!        S r"Sr#U =r$$ )!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#  r    r  r$  r   Nc                ó*   >• [         TU ]  " SXS.UD6  g )Nr  r1   r2   )r4   r  r  r(   r)   s       €r*   r3   ÚUniform.__init__p  ó   ø€ Ü‰ÒÐ,˜1Ñ, VÓ,r,   c                 ó@   • X!-
  nUR                  [        XUS95        U$ )N)r  r  Úab)r,  r-  ©r4   r  r  rF  r(   s        r*   r.  ÚUniform._process_parameterss  s!   € Ø‰UˆØ�‰”d˜Q¨Ñ+Ô,Øˆr,   c                ó    • [         R                  " [         R                  " U5      [         R                  [         R                  " U5      * 5      $ r#   )r8   ÚwhereÚisnanÚnanr9   ©r4   r   rF  r(   s       r*   r7   ÚUniform._logpdf_formulax  s+   € Ü�xŠxœŸš ›¤R§V¡V¬b¯fªf°R«j¨[Ó9Ð9r,   c                ó|   • [         R                  " [         R                  " U5      [         R                  SU-  5      $ ©Nr   )r8   rJ  rK  rL  rM  s       r*   r=   ÚUniform._pdf_formula{  s%   € Ü�xŠxœŸš ›¤R§V¡V¨Q¨r©TÓ2Ð2r,   c                ó¾   • [         R                  " SS9   [         R                  " X-
  5      [         R                  " U5      -
  sS S S 5        $ ! , (       d  f       g = f©Nr]   r^   ©r8   rc   r9   ©r4   r   r  rF  r(   s        r*   r@   ÚUniform._logcdf_formula~  ó4   € Ü�[Š[ Ó)Ü—6’6˜!™%“=¤2§6¢6¨"£:Ñ-÷ *×)×)úó   •/AÁ
Ac                ó   • X-
  U-  $ r#   r1   rU  s        r*   rC   ÚUniform._cdf_formula‚  ó   € Ø‘˜‰|Ðr,   c                ó¾   • [         R                  " SS9   [         R                  " X!-
  5      [         R                  " U5      -
  sS S S 5        $ ! , (       d  f       g = frS  rT  ©r4   r   r  rF  r(   s        r*   rF   ÚUniform._logccdf_formula…  rW  rX  c                ó   • X!-
  U-  $ r#   r1   r]  s        r*   rI   ÚUniform._ccdf_formula‰  r[  r,   c                ó   • X#U-  -   $ r#   r1   )r4   Úpr  rF  r(   s        r*   rL   ÚUniform._icdf_formulaŒ  ó   € Ø�a‘4‰xˆr,   c                ó   • X#U-  -
  $ r#   r1   )r4   rb  r  rF  r(   s        r*   rR   ÚUniform._iccdf_formula�  rd  r,   c                ó.   • [         R                  " U5      $ r#   r  )r4   rF  r(   s      r*   rX   ÚUniform._entropy_formula’  s   € Ü�vŠv�b‹zÐr,   c                ó   • USU-  -   $ ©Nr   r1   rG  s        r*   rn   ÚUniform._mode_formula•  ó   € Ø�3�r‘6‰zÐr,   c                ó   • USU-  -   $ rj  r1   rG  s        r*   rj   ÚUniform._median_formula˜  rl  r,   c                 ó(   • US-   nX6-  X&-  -
  Xd-  -  $ rP  r1   )r4   rs   r  r  rF  r(   Únp1s          r*   rt   ÚUniform._moment_raw_formula›  s    € Ø�a‰iˆØ‘˜™‘ C¡HÑ-Ð-r,   c                 ó"   • US:X  a  US-  S-  $ S $ )Nr!   é   r1   )r4   rs   rF  r(   s       r*   r{   ÚUniform._moment_central_formulaŸ  s   € Ø  A›:ˆr�1‰u�R‰xÐ/¨4Ð/r,   r!   c                 óx   •  UR                  X4US9S   $ ! [         a    UR                  SSUS9U-  U-   s $ f = f)Nrå   r1   r   r   )ÚuniformÚOverflowError)r4   rƒ   r„   r  r  rF  r(   s          r*   r…   ÚUniform._sample_formula¤  sM   € ð	=Ø—;‘;˜q¨*�;Ð5°bÑ9Ð9øÜó 	=Ø—;‘;˜q !¨*�;Ð5°bÑ8¸1Ñ<Ò<ð	=ús   ‚ •!9¸9r1   )NNN)%r‡   rˆ   r‰   rŠ   r‹   r	   r   r8  r9  rŽ   r   r<  r=  r‘   r@  r   r’   r“   r3   r.  r7   r=   r@   rC   rF   rI   rL   rR   rX   rn   rj   rt   r{   r˜   r…   r™   rš   r›   s   @r*   r   r   V  sý   ø† ñ	ñ ¨#¨¨s¨Ñ4€IÙ¨¨c¨
Ñ3€IÙ¨¸|ÑL€Já˜c¨)¸[ÑI€HÙ˜c¨)¸ZÑH€HÙ˜c¨*¸jÑI€Hà×Ñ Ô)Ø× Ñ  ¨8Ô4á+¨H°hÓ?Ð@ÐØ€Ià  D÷ -ð -ôò
:ò3ò.òò.òòòòòòò.ò0ð '( SÐÔ"÷=ð =r,   r   c                   ór   • \ rS rSr\" S\4S9r\" S\4SS9r\" S\SS9r	\" S	\SS9r
\" \	5      /r\
rS
 rSrg)Ú_Gammai«  r   r   ©FFr!  r  )r'  é
   r    r   c                ón   • XS-
  -  [         R                  " U* 5      -  [        R                  " U5      -  $ rP  )r8   r¬   r   Úgamma)r4   r   r  r(   s       r*   r=   Ú_Gamma._pdf_formula¶  s+   € Ø˜‘U‰|œbŸfšf a R›jÑ(¬7¯=ª=¸Ó+;Ñ;Ð;r,   r1   N)r‡   rˆ   r‰   rŠ   r	   r   r8  rŽ   r   r<  r‘   r   r’   r“   r=   r™   r1   r,   r*   rz  rz  «  sT   † á¨¨C¨Ñ1€IÙ¨!¨S¨¸^ÑL€Já˜c¨)¸YÑG€HÙ˜c¨*¸iÑH€Há+¨HÓ5Ð6ÐØ€Iõ<r,   rz  c                   ó  ^ • \ rS rSrSr\" S\4SS9r\" SSS9r	\" SSS9r
\" S	\S
S9r\" S\	SS9r\" S\
SS9r\" \\5      /r\rU 4S jrS rS rS rS rS rS rS rS rS rS rSS/\l        S r/ SQ\l        SrU =r $ ) 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   )r   r  r   r  )r|  é   r    rb  )g      Ð?g      è?r   )r   r|  c                ó*   >• [         TU ]  " SXS.UD6  g )N©r  rb  r1   r2   )r4   r  rb  r(   r)   s       €r*   r3   ÚBinomial.__init__Ï  rD  r,   c                ó0   • [         R                  " XU5      $ r#   )ÚscuÚ
_binom_pmf©r4   r   r  rb  r(   s        r*   Ú_pmf_formulaÚBinomial._pmf_formulaÒ  ó   € Ü�~Š~˜a AÓ&Ð&r,   c                ó  • [         R                  " US-   5      [         R                  " US-   5      [         R                  " X!-
  S-   5      -   -
  nU[         R                  " X5      -   [         R                  " X!-
  U* 5      -   $ rP  )r   ÚgammalnÚxlogyÚxlog1py)r4   r   r  rb  r(   Úcombilns         r*   Ú_logpmf_formulaÚBinomial._logpmf_formulaÕ  si   € ô
 �OŠO˜A˜a™CÓ ¤G§O¢O°A°a±CÓ$8¼7¿?º?È1É3ÈqÉ5Ó;QÑ$QÑRð 	ð œŸš qÓ,Ñ,¬w¯ª¸q¹sÀQÀBÓ/GÑGÐGr,   c                ó0   • [         R                  " XU5      $ r#   )r†  Ú
_binom_cdfrˆ  s        r*   rC   ÚBinomial._cdf_formulaÞ  r‹  r,   c                ó`   • U R                  SX#S9n[        R                  " X:  XU4S S 5      $ )Nr   rƒ  c                  óP   • [         R                  " [        R                  " U 6 5      $ r#   )r8   r9   r†  r”  ©Úargss    r*   Ú<lambda>Ú*Binomial._logcdf_formula.<locals>.<lambda>æ  s   € œ"Ÿ&š&¤§¢°Ð!6Ô7r,   c                  óR   • [         R                  " [        R                  " U 6 * 5      $ r#   )r8   rÍ   r†  Ú	_binom_sfr˜  s    r*   rš  r›  ç  s   € œ"Ÿ(š(¤C§M¢M°4Ð$8Ð#8Ô9r,   ©rL   ÚxpxÚapply_where©r4   r   r  rb  r(   Úmedians         r*   r@   ÚBinomial._logcdf_formulaá  s:   € ð ×#Ñ# C¨1Ð#Ð2ˆÜ�Š˜q™z¨A°!¨9Ù7Ù9ó
ð 	
r,   c                ó0   • [         R                  " XU5      $ r#   )r†  r�  rˆ  s        r*   rI   ÚBinomial._ccdf_formulaê  s   € Ü�}Š}˜Q 1Ó%Ð%r,   c                ó`   • U R                  SX#S9n[        R                  " X:  XU4S S 5      $ )Nr   rƒ  c                  óR   • [         R                  " [        R                  " U 6 * 5      $ r#   )r8   rÍ   r†  r”  r˜  s    r*   rš  Ú+Binomial._logccdf_formula.<locals>.<lambda>ð  s   € œ"Ÿ(š(¤C§N¢N°DÐ$9Ð#9Ô:r,   c                  óP   • [         R                  " [        R                  " U 6 5      $ r#   )r8   r9   r†  r�  r˜  s    r*   rš  r¨  ñ  s   € œ"Ÿ&š&¤§¢°Ð!5Ô6r,   rž  r¡  s         r*   rF   ÚBinomial._logccdf_formulaí  s8   € Ø×#Ñ# C¨1Ð#Ð2ˆÜ�Š˜q™z¨A°!¨9Ù:Ù6ó
ð 	
r,   c                ó0   • [         R                  " XU5      $ r#   )r†  Ú
_binom_ppfrˆ  s        r*   rL   ÚBinomial._icdf_formulaô  r‹  r,   c                ó0   • [         R                  " XU5      $ r#   )r†  Ú
_binom_isfrˆ  s        r*   rR   ÚBinomial._iccdf_formula÷  r‹  r,   c                ó€   • [         R                  " US-   U-  5      n[         R                  " US:H  US-
  U5      nUS   $ )Nr   r1   )r8   ÚfloorrJ  )r4   r  rb  r(   Úmodes        r*   rn   ÚBinomial._mode_formulaú  s;   € ä�xŠx˜˜1™˜a™Ó ˆÜ�xŠx˜˜Q™  q¡¨$Ó/ˆØ�B‰xˆr,   c                óB   • US:X  a  X#-  $ US:X  a  X#-  SU-
  X#-  -   -  $ g rÊ   r1   ©r4   rs   r  rb  r(   s        r*   rt   ÚBinomial._moment_raw_formula   s1   € à�A‹:Ø‘3ˆJØ�A‹:Ø‘3˜˜A™ ¡™Ñ$Ð$Ør,   r   r!   c                óØ   • US:X  a  [         R                  " U5      $ US:X  a
  X#-  SU-
  -  $ US:X  a  X#-  SU-
  -  SSU-  -
  -  $ US:X  a  X#-  SU-
  -  SSU-  S-
  U-  SU-
  -  -   -  $ g )Nr   r!   rÖ   r×   é   )r8   rx   r¶  s        r*   r{   Ú Binomial._moment_central_formula	  sŒ   € à�A‹:Ü—=’= Ó#Ð#Ø�A‹:Ø‘3˜˜A™‘;ÐØ�A‹:Ø‘3˜˜A™‘;  A a¡C¡Ñ(Ð(Ø�A‹:Ø‘3˜˜A™‘;  Q q¡S¨1¡W¨a¡K°°Q±Ñ$7Ñ 7Ñ8Ð8Ør,   )r   r!   rÖ   r×   r1   )!r‡   rˆ   r‰   rŠ   r‹   r
   r   Ú	_n_domainr	   Ú	_p_domainrŽ   r   Ú_n_paramÚ_p_paramr‘   r   r’   r“   r3   r‰  r‘  rC   r@   rI   rF   rL   rR   rn   rt   r˜   r{   r™   rš   r›   s   @r*   r   r   º  sË   ø† ññ !¨A¨s¨8¸~ÑN€IÙ¨¸.ÑI€IÙ!¨HÀÑM€Já˜c¨)¸XÑF€HÙ˜c¨)¸\ÑJ€HÙ˜c¨*¸gÑF€Há+¨H°hÓ?Ð@ÐØ€Iõ-ò'òHò'ò
ò&ò
ò'ò'òòð #$ Q ÐÔò
ò &2Ð×"Ò"r,   r   )#ÚsysÚnumpyr8   r   Ú
scipy._libr   rŸ  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   rz  r   Úmodulesr‡   Ú__dict__Ú_moduleÚ	dist_namer‹   r1   r,   r*   Ú<module>rÊ     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@ �+‰+�hÑ
×
(Ñ
(€Û€IÙ!.¨w°yÑ/AÓ!B€GˆIÑÖò r,   