§
    µ³Ùg·3  ã                   óJ  — d dl Z d dlZd dlmZ d dlmZ d dlmZmZm	Z	m
Z
mZ ddgZ G d„ de¦  «        Zd„ Z G d	„ d
e¦  «        Z G d„ de¦  «        Z G d„ de¦  «        Z G d„ de¦  «        Ze j        e         j        ZeD ]Z eee         ¦  «        ee         _        ŒdS )é    N)Úinf)Úspecial)ÚContinuousDistributionÚ_RealDomainÚ_RealParameterÚ_ParameterizationÚ_combine_docsÚNormalÚUniformc                   óè  ‡ — e Zd ZdZ ee ef¬¦  «        Z edef¬¦  «        Z ee ef¬¦  «        Z e	dded¬¦  «        Z
 e	dd	ed
¬¦  «        Z e	ded¬¦  «        Z ee
e¦  «        gZeZd ej        dej        z  ¦  «        z  Z ej        dej        z  ¦  «        dz  Zd&ˆ fd„	Zdddœˆ fd„
Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z d„ Z!d„ Z"d „ Z#d!„ Z$d"„ Z%d#„ Z&ddge&_'        d$„ Z(d%„ Z)ˆ xZ*S )'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	endpointsr   Úmuz\mu)éÿÿÿÿé   ©ÚsymbolÚdomainÚtypicalÚsigmaz\sigma)ç      à?g      ø?Úx©r   r   r   é   Nc                 óš   •— |€(|€&t          ¦   «                              t          ¦  «        S t          ¦   «                              | ¦  «        S ©N)ÚsuperÚ__new__ÚStandardNormal)Úclsr   r   ÚkwargsÚ	__class__s       €úT/granary/edev/quantum/lib/python3.11/site-packages/scipy/stats/_new_distributions.pyr   zNormal.__new__,   s8   ø€ Øˆ:˜%˜-Ý‘7”7—?’?¥>Ñ2Ô2Ð2Ý‰wŒw�Š˜sÑ#Ô#Ð#ó    ç        ç      ð?©r   r   c                ó@   •—  t          ¦   «         j        d||dœ|¤Ž d S )Nr'   © ©r   Ú__init__)Úselfr   r   r!   r"   s       €r#   r+   zNormal.__init__1   s-   ø€ Ø�‰ŒÔÐ6˜B eÐ6Ð6¨vÐ6Ð6Ð6Ð6Ð6r$   c                ón   — t                                | ||z
  |z  ¦  «        t          j        |¦  «        z
  S r   )r   Ú_logpdf_formulaÚnpÚlog©r,   r   r   r   r!   s        r#   r.   zNormal._logpdf_formula4   s-   € Ý×-Ò-¨d°Q¸±V¸U±NÑCÔCÅbÄfÈUÁmÄmÑSÐSr$   c                óJ   — t                                | ||z
  |z  ¦  «        |z  S r   )r   Ú_pdf_formular1   s        r#   r3   zNormal._pdf_formula7   s%   € Ý×*Ò*¨4°!°b±&¸%±Ñ@Ô@À5ÑHÐHr$   c                óD   — t                                | ||z
  |z  ¦  «        S r   )r   Ú_logcdf_formular1   s        r#   r5   zNormal._logcdf_formula:   s    € Ý×-Ò-¨d°Q¸±V¸U±NÑCÔCÐCr$   c                óD   — t                                | ||z
  |z  ¦  «        S r   )r   Ú_cdf_formular1   s        r#   r7   zNormal._cdf_formula=   s    € Ý×*Ò*¨4°!°b±&¸%±Ñ@Ô@Ð@r$   c                óD   — t                                | ||z
  |z  ¦  «        S r   )r   Ú_logccdf_formular1   s        r#   r9   zNormal._logccdf_formula@   s    € Ý×.Ò.¨t°a¸"±f¸e±^ÑDÔDÐDr$   c                óD   — t                                | ||z
  |z  ¦  «        S r   )r   Ú_ccdf_formular1   s        r#   r;   zNormal._ccdf_formulaC   s    € Ý×+Ò+¨D°1°r±6¸5±.ÑAÔAÐAr$   c                óD   — t                                | |¦  «        |z  |z   S r   )r   Ú_icdf_formular1   s        r#   r=   zNormal._icdf_formulaF   s"   € Ý×+Ò+¨D°!Ñ4Ô4°uÑ<¸rÑAÐAr$   c                óD   — t                                | |¦  «        |z  |z   S r   )r   Ú_ilogcdf_formular1   s        r#   r?   zNormal._ilogcdf_formulaI   s"   € Ý×.Ò.¨t°QÑ7Ô7¸%Ñ?À"ÑDÐDr$   c                óD   — t                                | |¦  «        |z  |z   S r   )r   Ú_iccdf_formular1   s        r#   rA   zNormal._iccdf_formulaL   s"   € Ý×,Ò,¨T°1Ñ5Ô5¸Ñ=ÀÑBÐBr$   c                óD   — t                                | |¦  «        |z  |z   S r   )r   Ú_ilogccdf_formular1   s        r#   rC   zNormal._ilogccdf_formulaO   s"   € Ý×/Ò/°°aÑ8Ô8¸5Ñ@À2ÑEÐEr$   c                óz   — t                                | ¦  «        t          j        t	          |¦  «        ¦  «        z   S r   )r   Ú_entropy_formular/   r0   Úabs©r,   r   r   r!   s       r#   rE   zNormal._entropy_formulaR   s+   € Ý×.Ò.¨tÑ4Ô4µr´v½cÀ%¹j¼jÑ7IÔ7IÑIÐIr$   c                óN  — t                                | ¦  «        }t          j        d¬¦  «        5  t          j        t          j        t          |¦  «        ¦  «        dz   ¦  «        }d d d ¦  «         n# 1 swxY w Y   t          j        t          j        ||¦  «        d¬¦  «        S )NÚignore©Údividey                r   ©Úaxis)	r   Ú_logentropy_formular/   Úerrstater0   rF   r   Ú	logsumexpÚbroadcast_arrays)r,   r   r   r!   ÚlH0Úllss         r#   rN   zNormal._logentropy_formulaU   sÈ   € Ý×0Ò0°Ñ6Ô6ˆÝŒ[ Ð)Ñ)Ô)ð 	0ð 	0õ ”&�œ¥ E¡
¤
Ñ+Ô+¨BÑ.Ñ/Ô/ˆCð	0ð 	0ð 	0ñ 	0ô 	0ð 	0ð 	0ð 	0ð 	0ð 	0ð 	0øøøð 	0ð 	0ð 	0ð 	0õ Ô ¥Ô!4°S¸#Ñ!>Ô!>ÀQÐGÑGÔGÐGs   °7A3Á3A7Á:A7c                ó   — |S r   r)   rG   s       r#   Ú_median_formulazNormal._median_formula]   ó   € Øˆ	r$   c                ó   — |S r   r)   rG   s       r#   Ú_mode_formulazNormal._mode_formula`   rV   r$   c                óJ   — |dk    rt          j        |¦  «        S |dk    r|S d S )Nr   r   )r/   Ú	ones_like©r,   Úorderr   r   r!   s        r#   Ú_moment_raw_formulazNormal._moment_raw_formulac   s.   € Ø�AŠ:ˆ:Ý”< Ñ#Ô#Ð#Ø�aŠZˆZØˆIà�4r$   c                óÀ   — |dk    rt          j        |¦  «        S |dz  rt          j        |¦  «        S ||z  t          j        t          |¦  «        dz
  d¬¦  «        z  S )Nr   r   r   T)Úexact)r/   rZ   Ú
zeros_liker   Ú
factorial2Úintr[   s        r#   Ú_moment_central_formulazNormal._moment_central_formulal   sc   € Ø�AŠ:ˆ:Ý”< Ñ#Ô#Ð#Ø�Q‰Yð 	QÝ”= Ñ$Ô$Ð$ð ˜%‘<¥'Ô"4µS¸±Z´ZÀ!±^È4Ð"PÑ"PÔ"PÑPÐPr$   c                ó>   — |                      |||¬¦  «        d         S )N)ÚlocÚscaleÚsizer)   ©Únormal)r,   Úsample_shapeÚ
full_shapeÚrngr   r   r!   s          r#   Ú_sample_formulazNormal._sample_formulau   s   € Ø�zŠz˜b¨°JˆzÑ?Ô?ÀÔCÐCr$   )NN)+Ú__name__Ú
__module__Ú__qualname__Ú__doc__r   r   Ú
_mu_domainÚ_sigma_domainÚ
_x_supportr   Ú	_mu_paramÚ_sigma_paramÚ_x_paramr   Ú_parameterizationsÚ	_variabler/   ÚsqrtÚpiÚ_normalizationr0   Ú_log_normalizationr   r+   r.   r3   r5   r7   r9   r;   r=   r?   rA   rC   rE   rN   rU   rX   r]   Úordersrc   rm   Ú__classcell__©r"   s   @r#   r
   r
      s›  ø€ € € € € ð	ð 	ð �¨¨¨c {Ð3Ñ3Ô3€JØ�K¨1¨c¨(Ð3Ñ3Ô3€MØ�¨¨¨c {Ð3Ñ3Ô3€Jà�˜t¨V¸JØ'.ð0ñ 0ô 0€Ià!�> '°)ÀMØ*4ð6ñ 6ô 6€Làˆ~˜c¨*¸gÐFÑFÔF€Hà+Ð+¨I°|ÑDÔDÐEÐà€IØ�w�r”w˜q ¤™wÑ'Ô'Ñ'€NØ˜œ  "¤%¡™œ¨Ñ*Ðð$ð $ð $ð $ð $ð $ð
   rð 7ð 7ð 7ð 7ð 7ð 7ð 7ðTð Tð TðIð Ið IðDð Dð DðAð Að AðEð Eð EðBð Bð BðBð Bð BðEð Eð EðCð Cð CðFð Fð FðJð Jð JðHð Hð Hðð ð ðð ð ðð ð ð #$ Q ÐÔðQð Qð QðDð Dð Dð Dð Dð Dð Dr$   c                 óR   — t          j        | |t          j        dz  z   gd¬¦  «        S )Ny              ð?r   rL   )r   rP   r/   r{   )Úlog_pÚlog_qs     r#   Ú	_log_diffr„   y   s'   € ÝÔ˜e U­2¬5°©8¡^Ð4¸1Ð=Ñ=Ô=Ð=r$   c                   ór  — e Zd ZdZ ee ef¬¦  «        Z eded¬¦  «        ZeZ	g Z
d ej        dej        z  ¦  «        z  Z ej        dej        z  ¦  «        dz  Z ej        d¦  «        Z ej        d	¦  «        Zd
„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Z d„ Z!d„ Z"d„ Z#d„ Z$d„ Z%d„ Z&dS )r   zÌStandard 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                 ó*   — t          j        | fi |¤Ž d S r   )r   r+   ©r,   r!   s     r#   r+   zStandardNormal.__init__�   s!   € ÝÔ'¨Ð7Ð7°Ð7Ð7Ð7Ð7Ð7r$   c                 ó$   — | j         |dz  dz  z    S ©Nr   )r}   ©r,   r   r!   s      r#   r.   zStandardNormal._logpdf_formula“   s   € ØÔ(¨1¨a©4°©6Ñ1Ð2Ð2r$   c                 óH   — | j         t          j        |dz   dz  ¦  «        z  S r‹   )r|   r/   ÚexprŒ   s      r#   r3   zStandardNormal._pdf_formula–   s"   € ØÔ"¥R¤V¨Q°©T¨E°!©G¡_¤_Ñ4Ð4r$   c                 ó*   — t          j        |¦  «        S r   ©r   Úlog_ndtrrŒ   s      r#   r5   zStandardNormal._logcdf_formula™   s   € ÝÔ Ñ"Ô"Ð"r$   c                 ó*   — t          j        |¦  «        S r   ©r   ÚndtrrŒ   s      r#   r7   zStandardNormal._cdf_formulaœ   s   € ÝŒ|˜A‰ŒÐr$   c                 ó,   — t          j        | ¦  «        S r   r�   rŒ   s      r#   r9   zStandardNormal._logccdf_formulaŸ   s   € ÝÔ  Ñ#Ô#Ð#r$   c                 ó,   — t          j        | ¦  «        S r   r“   rŒ   s      r#   r;   zStandardNormal._ccdf_formula¢   s   € ÝŒ|˜Q˜BÑÔÐr$   c                 ó*   — t          j        |¦  «        S r   ©r   ÚndtrirŒ   s      r#   r=   zStandardNormal._icdf_formula¥   s   € ÝŒ}˜QÑÔÐr$   c                 ó*   — t          j        |¦  «        S r   ©r   Ú	ndtri_exprŒ   s      r#   r?   zStandardNormal._ilogcdf_formula¨   s   € ÝÔ  Ñ#Ô#Ð#r$   c                 ó,   — t          j        |¦  «         S r   r˜   rŒ   s      r#   rA   zStandardNormal._iccdf_formula«   s   € Ý”˜aÑ Ô Ð Ð r$   c                 ó,   — t          j        |¦  «         S r   r›   rŒ   s      r#   rC   z StandardNormal._ilogccdf_formula®   s   € ÝÔ! !Ñ$Ô$Ð$Ð$r$   c                 óP   — dt          j        dt           j        z  ¦  «        z   dz  S )Nr   r   )r/   r0   r{   r‰   s     r#   rE   zStandardNormal._entropy_formula±   s    € Ø•B”F˜1�RœU™7‘O”OÑ# QÑ&Ð&r$   c                 ó’   — t          j        t          j        dt           j        z  ¦  «        ¦  «        t          j        d¦  «        z
  S r‹   )r/   Úlog1pr0   r{   r‰   s     r#   rN   z"StandardNormal._logentropy_formula´   s-   € ÝŒx�œ˜q¥¤™w™œÑ(Ô(­2¬6°!©9¬9Ñ4Ð4r$   c                 ó   — dS ©Nr   r)   r‰   s     r#   rU   zStandardNormal._median_formula·   ó   € Øˆqr$   c                 ó   — dS r£   r)   r‰   s     r#   rX   zStandardNormal._mode_formulaº   r¤   r$   c                 ó@   — dddddddœ}|                      |d ¦  «        S )Nr   r   é   )r   r   r   r§   é   r‡   )Úget)r,   r\   r!   Úraw_momentss       r#   r]   z"StandardNormal._moment_raw_formula½   s+   € Ø  a¨A°!¸Ð:Ð:ˆØ�Š˜u dÑ+Ô+Ð+r$   c                 ó   —  | j         |fi |¤ŽS r   ©r]   ©r,   r\   r!   s      r#   rc   z&StandardNormal._moment_central_formulaÁ   ó   € Ø'ˆtÔ'¨Ð8Ð8°Ð8Ð8Ð8r$   c                 ó   —  | j         |fi |¤ŽS r   r¬   r­   s      r#   Ú_moment_standardized_formulaz+StandardNormal._moment_standardized_formulaÄ   r®   r$   c                 ó:   — |                      |¬¦  «        d         S )N©rg   r)   rh   )r,   rj   rk   rl   r!   s        r#   rm   zStandardNormal._sample_formulaÇ   s   € Ø�zŠz˜zˆzÑ*Ô*¨2Ô.Ð.r$   N)'rn   ro   rp   rq   r   r   rt   r   rw   ry   rx   r/   rz   r{   r|   r0   r}   Úfloat64r   r   r+   r.   r3   r5   r7   r9   r;   r=   r?   rA   rC   rE   rN   rU   rX   r]   rc   r°   rm   r)   r$   r#   r   r   }   sË  € € € € € ðð ð �¨¨¨c {Ð3Ñ3Ô3€JØˆ~˜c¨*¸gÐFÑFÔF€HØ€IØÐØ�w�r”w˜q ¤™wÑ'Ô'Ñ'€NØ˜œ  "¤%¡™œ¨Ñ*ÐØ	ˆŒ�B‰Œ€BØˆBŒJ�r‰NŒN€Eð8ð 8ð 8ð3ð 3ð 3ð5ð 5ð 5ð#ð #ð #ðð ð ð$ð $ð $ð ð  ð  ð ð  ð  ð$ð $ð $ð!ð !ð !ð%ð %ð %ð'ð 'ð 'ð5ð 5ð 5ðð ð ðð ð ð,ð ,ð ,ð9ð 9ð 9ð9ð 9ð 9ð/ð /ð /ð /ð /r$   r   c                   ó  ‡ — e Zd ZdZ edef¬¦  «        Z edef¬¦  «        Z ee ef¬¦  «        Z edef¬¦  «        Z	 edd¬¦  «        Z
 eded	¬
¦  «        Z eded¬
¦  «        Z edded¬¦  «        Z edde	d¬¦  «        Z ede
d¬
¦  «        Ze                     e¦  «         e	                     e¦  «         e
                     ee¦  «          eee¦  «         eee¦  «        gZeZdddddœˆ fd„
Zdd„Zd„ Zd„ Zˆ xZS )Ú_LogUniformaª  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   r¹   ©gš™™™™™ñ?g     @�@z\log(a))éýÿÿÿgš™™™™™¹¿r   Úlog_bz\log(b))çš™™™™™¹?r§   r   N©r¶   r¹   r·   rÀ   c                óD   •—  t          ¦   «         j        d||||dœ|¤Ž d S )NrÂ   r)   r*   )r,   r¶   r¹   r·   rÀ   r!   r"   s         €r#   r+   z_LogUniform.__init__ò   s1   ø€ Ø�‰ŒÔÐF˜1 ¨°eÐFÐF¸vÐFÐFÐFÐFÐFr$   c                 ó  — |€t          j        |¦  «        n|}|€t          j        |¦  «        n|}|€t          j        |¦  «        n|}|€t          j        |¦  «        n|}|                     t	          ||||¬¦  «        ¦  «         |S )NrÂ   )r/   rŽ   r0   ÚupdateÚdict)r,   r¶   r¹   r·   rÀ   r!   s         r#   Ú_process_parametersz_LogUniform._process_parametersõ   s~   € Ø˜Y�BŒF�5‰MŒMˆM¨AˆØ˜Y�BŒF�5‰MŒMˆM¨AˆØ"˜]•”�q‘	”	�	°ˆØ"˜]•”�q‘	”	�	°ˆØ�Š•d˜Q !¨5¸Ð>Ñ>Ô>Ñ?Ô?Ð?Øˆr$   c                ó   — ||z
  |z  dz  S )Nr   r)   )r,   r   r·   rÀ   r!   s        r#   r3   z_LogUniform._pdf_formula   s   € Ø˜‘ Ñ! BÑ&Ð&r$   c           	      óº   — |dk    r| j         S | j         ||z
  z  |z  }t          j        t          j        t	          ||z  ||z  ¦  «        ¦  «        ¦  «        }||z  S r£   )Ú_oner/   ÚrealrŽ   r„   )r,   r\   r·   rÀ   r!   Út1Út2s          r#   r]   z_LogUniform._moment_raw_formula  s\   € Ø�AŠ:ˆ:Ø”9ÐØŒY˜% %™-Ñ(¨5Ñ0ˆÝŒW•R”V�I e¨e¡m°U¸U±]ÑCÔCÑDÔDÑEÔEˆØ�B‰wˆr$   )NNNN)rn   ro   rp   rq   r   r   Ú	_a_domainÚ	_b_domainÚ_log_a_domainÚ_log_b_domainrt   r   Ú_a_paramÚ_b_paramÚ_log_a_paramÚ_log_b_paramrw   Údefine_parametersr   rx   ry   r+   rÇ   r3   r]   r   r€   s   @r#   rµ   rµ   Ì   sð  ø€ € € € € ðð ð � q¨# hÐ/Ñ/Ô/€IØ� s¨C jÐ1Ñ1Ô1€IØ�K¨C¨4°¨+Ð6Ñ6Ô6€MØ�K¨7°C¨.Ð9Ñ9Ô9€MØ� z¸\ÐJÑJÔJ€Jàˆ~˜c¨)¸[ÐIÑIÔI€HØˆ~˜c¨)¸ZÐHÑHÔH€HØ!�> '°*Ø)6À
ðLñ Lô L€Là!�> '°*Ø)6ÀðJñ Jô J€Làˆ~˜c¨*¸jÐIÑIÔI€Hà×Ò Ñ)Ô)Ð)Ø×#Ò# LÑ1Ô1Ð1Ø× Ò  ¨8Ñ4Ô4Ð4à+Ð+¨L¸,ÑGÔGØ+Ð+¨H°hÑ?Ô?ðAÐà€Ià  D°¸Dð Gð Gð Gð Gð Gð Gð Gðð ð ð ð'ð 'ð 'ðð ð ð ð ð ð r$   rµ   c                   ó²  ‡ — e Zd ZdZ ee ef¬¦  «        Z edef¬¦  «        Z edd¬¦  «        Z e	ded¬¦  «        Z
 e	d	ed
¬¦  «        Z e	ded¬¦  «        Ze                     e
¦  «         e                     e
e¦  «          ee
e¦  «        gZeZdddœˆ fd„
Zdd„Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zd„ Zdge_         d„ Z!ˆ xZ"S )r   z±Uniform distribution.

    The probability density function of the uniform distribution is:

    .. math::

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

    r   r¶   r¸   rº   r»   r½   r   r¹   r¾   r   Nc                ó@   •—  t          ¦   «         j        d||dœ|¤Ž d S )Nr¸   r)   r*   )r,   r¶   r¹   r!   r"   s       €r#   r+   zUniform.__init__(  s-   ø€ Ø�‰ŒÔÐ,˜1 Ð,Ð, VÐ,Ð,Ð,Ð,Ð,r$   c                 óZ   — ||z
  }|                      t          |||¬¦  «        ¦  «         |S )N)r¶   r¹   Úab)rÅ   rÆ   ©r,   r¶   r¹   rÚ   r!   s        r#   rÇ   zUniform._process_parameters+  s1   € Ø�‰UˆØ�Š•d˜Q !¨Ð+Ñ+Ô+Ñ,Ô,Ð,Øˆr$   c                óŒ   — t          j        t          j        |¦  «        t           j        t          j        |¦  «         ¦  «        S r   )r/   ÚwhereÚisnanÚnanr0   ©r,   r   rÚ   r!   s       r#   r.   zUniform._logpdf_formula0  s*   € ÝŒx�œ ™œ¥R¤V­b¬f°R©j¬j¨[Ñ9Ô9Ð9r$   c                ól   — t          j        t          j        |¦  «        t           j        d|z  ¦  «        S ©Nr   )r/   rÝ   rÞ   rß   rà   s       r#   r3   zUniform._pdf_formula3  s$   € ÝŒx�œ ™œ¥R¤V¨Q¨r©TÑ2Ô2Ð2r$   c                ó¸   — t          j        d¬¦  «        5  t          j        ||z
  ¦  «        t          j        |¦  «        z
  cd d d ¦  «         S # 1 swxY w Y   d S ©NrI   rJ   ©r/   rO   r0   ©r,   r   r¶   rÚ   r!   s        r#   r5   zUniform._logcdf_formula6  ó•   € ÝŒ[ Ð)Ñ)Ô)ð 	.ð 	.Ý”6˜!˜a™%‘=”=¥2¤6¨"¡:¤:Ñ-ð	.ð 	.ð 	.ð 	.ñ 	.ô 	.ð 	.ð 	.ð 	.ð 	.ð 	.ð 	.øøøð 	.ð 	.ð 	.ð 	.ð 	.ð 	.ó   –,AÁAÁAc                ó   — ||z
  |z  S r   r)   ræ   s        r#   r7   zUniform._cdf_formula:  ó   € Ø�A‘˜‰|Ðr$   c                ó¸   — t          j        d¬¦  «        5  t          j        ||z
  ¦  «        t          j        |¦  «        z
  cd d d ¦  «         S # 1 swxY w Y   d S rä   rå   ©r,   r   r¹   rÚ   r!   s        r#   r9   zUniform._logccdf_formula=  rç   rè   c                ó   — ||z
  |z  S r   r)   rì   s        r#   r;   zUniform._ccdf_formulaA  rê   r$   c                ó   — |||z  z   S r   r)   )r,   Úpr¶   rÚ   r!   s        r#   r=   zUniform._icdf_formulaD  ó   € Ø�2�a‘4‰xˆr$   c                ó   — |||z  z
  S r   r)   )r,   rï   r¹   rÚ   r!   s        r#   rA   zUniform._iccdf_formulaG  rð   r$   c                ó*   — t          j        |¦  «        S r   )r/   r0   )r,   rÚ   r!   s      r#   rE   zUniform._entropy_formulaJ  s   € ÝŒv�b‰zŒzÐr$   c                ó   — |d|z  z   S ©Nr   r)   rÛ   s        r#   rX   zUniform._mode_formulaM  ó   € Ø�3�r‘6‰zÐr$   c                ó   — |d|z  z   S rô   r)   rÛ   s        r#   rU   zUniform._median_formulaP  rõ   r$   c                 ó.   — |dz   }||z  ||z  z
  ||z  z  S râ   r)   )r,   r\   r¶   r¹   rÚ   r!   Únp1s          r#   r]   zUniform._moment_raw_formulaS  s&   € Ø�a‰iˆØ�3‘˜˜C™‘ C¨"¡HÑ-Ð-r$   c                 ó"   — |dk    r|dz  dz  nd S )Nr   é   r)   )r,   r\   rÚ   r!   s       r#   rc   zUniform._moment_central_formulaW  s   € Ø  Aš:˜:ˆr�1‰u�R‰xˆx¨4Ð/r$   r   c                 óœ   — 	 |                      |||¬¦  «        d         S # t          $ r! |                      dd|¬¦  «        |z  |z   cY S w xY w)Nr²   r)   r   r   )ÚuniformÚOverflowError)r,   rj   rk   rl   r¶   r¹   rÚ   r!   s           r#   rm   zUniform._sample_formula\  sg   € ð	=Ø—;’;˜q !¨*�;Ñ5Ô5°bÔ9Ð9øÝð 	=ð 	=ð 	=Ø—;’;˜q !¨*�;Ñ5Ô5°bÑ8¸1Ñ<Ð<Ð<Ð<ð	=øøøs   ‚   (AÁ
A)NNN)#rn   ro   rp   rq   r   r   rÎ   rÏ   rt   r   rÒ   rÓ   rw   rÖ   r   rx   ry   r+   rÇ   r.   r3   r5   r7   r9   r;   r=   rA   rE   rX   rU   r]   rc   r~   rm   r   r€   s   @r#   r   r     s  ø€ € € € € ð	ð 	ð �¨ t¨S kÐ2Ñ2Ô2€IØ� s¨C jÐ1Ñ1Ô1€IØ� z¸\ÐJÑJÔJ€Jàˆ~˜c¨)¸[ÐIÑIÔI€HØˆ~˜c¨)¸ZÐHÑHÔH€HØˆ~˜c¨*¸jÐIÑIÔI€Hà×Ò Ñ)Ô)Ð)Ø× Ò  ¨8Ñ4Ô4Ð4à+Ð+¨H°hÑ?Ô?Ð@ÐØ€Ià  Dð -ð -ð -ð -ð -ð -ð -ðð ð ð ð
:ð :ð :ð3ð 3ð 3ð.ð .ð .ðð ð ð.ð .ð .ðð ð ðð ð ðð ð ðð ð ðð ð ðð ð ð.ð .ð .ð0ð 0ð 0ð '( SÐÔ"ð=ð =ð =ð =ð =ð =ð =r$   c                   ó¢   — e Zd Z edef¬¦  «        Z edefd¬¦  «        Z eded¬¦  «        Z eded¬¦  «        Z	 e
e¦  «        gZe	Zd	„ Zd
S )Ú_Gammar   r   )FFr»   r¶   )rÁ   é
   r   r   c                óh   — ||dz
  z  t          j        | ¦  «        z  t          j        |¦  «        z  S râ   )r/   rŽ   r   Úgamma)r,   r   r¶   r!   s       r#   r3   z_Gamma._pdf_formulan  s.   € Ø�Q˜‘U‰|�bœf a R™jœjÑ(­7¬=¸Ñ+;Ô+;Ñ;Ð;r$   N)rn   ro   rp   r   r   rÎ   rt   r   rÒ   rw   r   rx   ry   r3   r)   r$   r#   rÿ   rÿ   c  s–   € € € € € à� q¨# hÐ/Ñ/Ô/€IØ�¨¨3 x¸>ÐJÑJÔJ€Jàˆ~˜c¨)¸YÐGÑGÔG€HØˆ~˜c¨*¸iÐHÑHÔH€Hà+Ð+¨HÑ5Ô5Ð6ÐØ€Ið<ð <ð <ð <ð <r$   rÿ   )ÚsysÚnumpyr/   r   Úscipyr   Ú(scipy.stats._distribution_infrastructurer   r   r   r   r	   Ú__all__r
   r„   r   rµ   r   rÿ   Úmodulesrn   Ú__dict__Ú_moduleÚ	dist_namerq   r)   r$   r#   ú<module>r     sæ  ðØ 
€
€
€
à Ð Ð Ð Ø Ð Ð Ð Ð Ð à Ð Ð Ð Ð Ð ðð ð ð ð ð ð ð ð ð ð ð ð ð ð �YÐ
€ðhDð hDð hDð hDð hDÐ#ñ hDô hDð hDðV>ð >ð >ðK/ð K/ð K/ð K/ð K/�Vñ K/ô K/ð K/ð^?ð ?ð ?ð ?ð ?Ð(ñ ?ô ?ð ?ðDR=ð R=ð R=ð R=ð R=Ð$ñ R=ô R=ð R=ðj<ð <ð <ð <ð <Ð#ñ <ô <ð <ð$ Œ+�hÔ
Ô
(€Øð Cð C€IØ!. ¨w°yÔ/AÑ!BÔ!B€GˆIÔÔÐðCð Cr$   