§
    fŠtjëI  ã                   ó¢  — d dl Z d dlZd dlmZ d dlmZ d dlmZ d dl	m
Z d dlmZmZmZmZmZmZmZ g d¢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 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array_api_extra)Úspecial)Ú_ufuncs)ÚContinuousDistributionÚDiscreteDistributionÚ_RealIntervalÚ_IntegerIntervalÚ_RealParameterÚ_ParameterizationÚ_combine_docs)ÚNormalÚLogisticÚUniformÚBinomialc                   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       €ú\/var/www/html/CA-Chatbot/venv/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)   r1   zNormal.__init__3   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©r2   r   r   r   r'   s        r)   r4   zNormal._logpdf_formula6   s-   € Ý×-Ò-¨d°Q¸±V¸U±NÑCÔCÅbÄfÈUÁmÄmÑSÐSr*   c                óJ   — t                                | ||z
  |z  ¦  «        |z  S r"   )r%   Ú_pdf_formular7   s        r)   r9   zNormal._pdf_formula9   s%   € Ý×*Ò*¨4°!°b±&¸%±Ñ@Ô@À5ÑHÐHr*   c                óD   — t                                | ||z
  |z  ¦  «        S r"   )r%   Ú_logcdf_formular7   s        r)   r;   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_formular7   s        r)   r=   zNormal._cdf_formula?   s    € Ý×*Ò*¨4°!°b±&¸%±Ñ@Ô@Ð@r*   c                óD   — t                                | ||z
  |z  ¦  «        S r"   )r%   Ú_logccdf_formular7   s        r)   r?   zNormal._logccdf_formulaB   s    € Ý×.Ò.¨t°a¸"±f¸e±^ÑDÔDÐDr*   c                óD   — t                                | ||z
  |z  ¦  «        S r"   )r%   Ú_ccdf_formular7   s        r)   rA   zNormal._ccdf_formulaE   s    € Ý×+Ò+¨D°1°r±6¸5±.ÑAÔAÐAr*   c                óD   — t                                | |¦  «        |z  |z   S r"   )r%   Ú_icdf_formular7   s        r)   rC   zNormal._icdf_formulaH   s"   € Ý×+Ò+¨D°!Ñ4Ô4°uÑ<¸rÑAÐAr*   c                óD   — t                                | |¦  «        |z  |z   S r"   )r%   Ú_ilogcdf_formular7   s        r)   rE   zNormal._ilogcdf_formulaK   s"   € Ý×.Ò.¨t°QÑ7Ô7¸%Ñ?À"ÑDÐDr*   c                óD   — t                                | |¦  «        |z  |z   S r"   )r%   Ú_iccdf_formular7   s        r)   rG   zNormal._iccdf_formulaN   s"   € Ý×,Ò,¨T°1Ñ5Ô5¸Ñ=ÀÑBÐBr*   c                óD   — t                                | |¦  «        |z  |z   S r"   )r%   Ú_ilogccdf_formular7   s        r)   rI   zNormal._ilogccdf_formulaQ   s"   € Ý×/Ò/°°aÑ8Ô8¸5Ñ@À2ÑEÐEr*   c                óz   — t                                | ¦  «        t          j        t	          |¦  «        ¦  «        z   S r"   )r%   Ú_entropy_formular5   r6   Úabs©r2   r   r   r'   s       r)   rK   zNormal._entropy_formulaT   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_formular5   Úerrstater6   rL   r   Ú	logsumexpÚbroadcast_arrays)r2   r   r   r'   ÚlH0Úllss         r)   rT   zNormal._logentropy_formulaW   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/   rM   s       r)   Ú_median_formulazNormal._median_formula_   ó   € Øˆ	r*   c                ó   — |S r"   r/   rM   s       r)   Ú_mode_formulazNormal._mode_formulab   r\   r*   c                óJ   — |dk    rt          j        |¦  «        S |dk    r|S d S )Nr   r   )r5   Ú	ones_like©r2   Úorderr   r   r'   s        r)   Ú_moment_raw_formulazNormal._moment_raw_formulae   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)r5   r`   Ú
zeros_liker   Ú
factorial2Úintra   s        r)   Ú_moment_central_formulazNormal._moment_central_formulan   sc   € Ø�AŠ:ˆ:Ý”< Ñ#Ô#Ð#Ø�Q‰Yð 	QÝ”= Ñ$Ô$Ð$ð ˜%‘<¥'Ô"4µS¸±Z´ZÀ!±^È4Ð"PÑ"PÔ"PÑPÐPr*   c                ó>   — |                      |||¬¦  «        d         S )N)ÚlocÚscaleÚsizer/   ©Únormal)r2   Ú
full_shapeÚrngr   r   r'   s         r)   Ú_sample_formulazNormal._sample_formulaw   s   € Ø�zŠz˜b¨°JˆzÑ?Ô?ÀÔCÐCr*   )NN)+Ú__name__Ú
__module__Ú__qualname__Ú__doc__r	   r   Ú
_mu_domainÚ_sigma_domainÚ
_x_supportr   Ú	_mu_paramÚ_sigma_paramÚ_x_paramr   Ú_parameterizationsÚ	_variabler5   ÚsqrtÚpiÚ_normalizationr6   Ú_log_normalizationr$   r1   r4   r9   r;   r=   r?   rA   rC   rE   rG   rI   rK   rT   r[   r^   rc   Úordersri   rr   Ú__classcell__©r(   s   @r)   r   r      s›  ø€ € € € € ð	ð 	ð �¨3¨$°¨Ð5Ñ5Ô5€JØ!�M¨Q°¨HÐ5Ñ5Ô5€MØ�¨3¨$°¨Ð5Ñ5Ô5€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*   r   c                 óR   — t          j        | |t          j        dz  z   gd¬¦  «        S )Ny              ð?r   rR   )r   rV   r5   r€   )Úlog_pÚlog_qs     r)   Ú	_log_diffr‰   {   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   r1   ©r2   r'   s     r)   r1   zStandardNormal.__init__’   s!   € ÝÔ'¨Ð7Ð7°Ð7Ð7Ð7Ð7Ð7r*   c                 ó$   — | j         |dz  dz  z    S ©Nr    )r‚   ©r2   r   r'   s      r)   r4   zStandardNormal._logpdf_formula•   s   € ØÔ(¨1¨a©4°©6Ñ1Ð2Ð2r*   c                 óH   — | j         t          j        |dz   dz  ¦  «        z  S r�   )r�   r5   Úexpr‘   s      r)   r9   zStandardNormal._pdf_formula˜   s"   € ØÔ"¥R¤V¨Q°©T¨E°!©G¡_¤_Ñ4Ð4r*   c                 ó*   — t          j        |¦  «        S r"   ©r   Úlog_ndtrr‘   s      r)   r;   zStandardNormal._logcdf_formula›   s   € ÝÔ Ñ"Ô"Ð"r*   c                 ó*   — t          j        |¦  «        S r"   ©r   Úndtrr‘   s      r)   r=   zStandardNormal._cdf_formulaž   s   € ÝŒ|˜A‰ŒÐr*   c                 ó,   — t          j        | ¦  «        S r"   r•   r‘   s      r)   r?   zStandardNormal._logccdf_formula¡   s   € ÝÔ  Ñ#Ô#Ð#r*   c                 ó,   — t          j        | ¦  «        S r"   r˜   r‘   s      r)   rA   zStandardNormal._ccdf_formula¤   s   € ÝŒ|˜Q˜BÑÔÐr*   c                 ó*   — t          j        |¦  «        S r"   ©r   Úndtrir‘   s      r)   rC   zStandardNormal._icdf_formula§   ó   € ÝŒ}˜QÑÔÐr*   c                 ó*   — t          j        |¦  «        S r"   ©r   Ú	ndtri_expr‘   s      r)   rE   zStandardNormal._ilogcdf_formulaª   ó   € ÝÔ  Ñ#Ô#Ð#r*   c                 ó,   — t          j        |¦  «         S r"   r�   r‘   s      r)   rG   zStandardNormal._iccdf_formula­   ó   € Ý”˜aÑ Ô Ð Ð r*   c                 ó,   — t          j        |¦  «         S r"   r¡   r‘   s      r)   rI   z StandardNormal._ilogccdf_formula°   s   € ÝÔ! !Ñ$Ô$Ð$Ð$r*   c                 óP   — dt          j        dt           j        z  ¦  «        z   dz  S ©Nr   r    )r5   r6   r€   rŽ   s     r)   rK   zStandardNormal._entropy_formula³   s    € Ø•B”F˜1�RœU™7‘O”OÑ# QÑ&Ð&r*   c                 ó’   — t          j        t          j        dt           j        z  ¦  «        ¦  «        t          j        d¦  «        z
  S r�   )r5   Úlog1pr6   r€   rŽ   s     r)   rT   z"StandardNormal._logentropy_formula¶   s-   € ÝŒx�œ˜q¥¤™w™œÑ(Ô(­2¬6°!©9¬9Ñ4Ð4r*   c                 ó   — dS ©Nr   r/   rŽ   s     r)   r[   zStandardNormal._median_formula¹   ó   € Øˆqr*   c                 ó   — dS r¬   r/   rŽ   s     r)   r^   zStandardNormal._mode_formula¼   r­   r*   c                 ó@   — dddddddœ}|                      |d ¦  «        S )Nr   r   é   )r   r   r    r°   é   rŒ   )Úget)r2   rb   r'   Úraw_momentss       r)   rc   z"StandardNormal._moment_raw_formula¿   s+   € Ø  a¨A°!¸Ð:Ð:ˆØ�Š˜u dÑ+Ô+Ð+r*   c                 ó   —  | j         |fi |¤ŽS r"   ©rc   ©r2   rb   r'   s      r)   ri   z&StandardNormal._moment_central_formulaÃ   ó   € Ø'ˆtÔ'¨Ð8Ð8°Ð8Ð8Ð8r*   c                 ó   —  | j         |fi |¤ŽS r"   rµ   r¶   s      r)   Ú_moment_standardized_formulaz+StandardNormal._moment_standardized_formulaÆ   r·   r*   c                 ó:   — |                      |¬¦  «        d         S ©N©rm   r/   rn   ©r2   rp   rq   r'   s       r)   rr   zStandardNormal._sample_formulaÉ   s   € Ø�zŠz˜zˆzÑ*Ô*¨2Ô.Ð.r*   N)'rs   rt   ru   rv   r	   r   ry   r   r|   r~   r}   r5   r   r€   r�   r6   r‚   Úfloat64r   r   r1   r4   r9   r;   r=   r?   rA   rC   rE   rG   rI   rK   rT   r[   r^   rc   ri   r¹   rr   r/   r*   r)   r%   r%      sË  € € € € € ðð ð �¨3¨$°¨Ð5Ñ5Ô5€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                   óä   — e Zd ZdZ ee ef¬¦  «        Z eded¬¦  «        xZZ	dZ
ej         ej        d¦  «        z  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   zÆStandard 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   r/   r°   c                 ó„   — t          j        |¦  «         }|dt          j        t          j        |¦  «        ¦  «        z  z
  S r�   )r5   rL   r   rª   r“   )r2   r   r'   Úys       r)   r4   zLogistic._logpdf_formulaÝ   s3   € ÝŒV�A‰YŒYˆJˆØ�1•w”}¥R¤V¨A¡Y¤YÑ/Ô/Ñ/Ñ/Ð/r*   c                 ó<   — dt          j        |dz  ¦  «        z  dz  S )Nr   r    )r5   Úcoshr‘   s      r)   r9   zLogistic._pdf_formulaá   s   € à•R”W˜Q ™U‘^”^Ñ# aÑ'Ð'r*   c                 ó*   — t          j        |¦  «        S r"   ©r   Ú	log_expitr‘   s      r)   r;   zLogistic._logcdf_formulaå   r£   r*   c                 ó*   — t          j        |¦  «        S r"   ©r   Úexpitr‘   s      r)   r=   zLogistic._cdf_formulaè   rŸ   r*   c                 ó,   — t          j        | ¦  «        S r"   rÆ   r‘   s      r)   r?   zLogistic._logccdf_formulaë   s   € ÝÔ  ! Ñ$Ô$Ð$r*   c                 ó,   — t          j        | ¦  «        S r"   rÉ   r‘   s      r)   rA   zLogistic._ccdf_formulaî   s   € ÝŒ}˜a˜RÑ Ô Ð r*   c                 ó*   — t          j        |¦  «        S r"   ©r   Úlogitr‘   s      r)   rC   zLogistic._icdf_formulañ   rŸ   r*   c                 ó,   — t          j        |¦  «         S r"   rÎ   r‘   s      r)   rG   zLogistic._iccdf_formulaô   r¥   r*   c                 ó   — dS )Ng       @r/   rŽ   s     r)   rK   zLogistic._entropy_formula÷   s   € Øˆsr*   c                 ó*   — t          j        d¦  «        S r�   ©r5   r6   rŽ   s     r)   rT   zLogistic._logentropy_formulaú   s   € ÝŒv�a‰yŒyÐr*   c                 ó   — dS r¬   r/   rŽ   s     r)   r[   zLogistic._median_formulaý   r­   r*   c                 ó   — dS r¬   r/   rŽ   s     r)   r^   zLogistic._mode_formula   r­   r*   c           	      óÈ   — t          |¦  «        }|dz  rdS t          j        |z  t          d|z  dz
  t	          t          j        |¦  «        d         ¦  «        z  ¦  «        z  S )Nr    r+   r   )rh   r5   r€   rL   Úfloatr   Ú	bernoulli)r2   rb   r'   Úns       r)   rc   zLogistic._moment_raw_formula  s\   € Ý�‰JŒJˆØˆq‰5ð 	Ø�3ÝŒu�a‰x�#˜q !™t a™x­5µÔ1BÀ1Ñ1EÔ1EÀbÔ1IÑ+JÔ+JÑJÑKÔKÑKÐKr*   c                 ó   —  | j         |fi |¤ŽS r"   rµ   r¶   s      r)   ri   z Logistic._moment_central_formula	  r·   r*   c                 ó4   —  | j         |fi |¤Ž| j        |z  z  S r"   )rc   Ú_scaler¶   s      r)   r¹   z%Logistic._moment_standardized_formula  s)   € Ø'ˆtÔ'¨Ð8Ð8°Ð8Ð8¸4¼;ÈÑ;MÑMÐMr*   c                 ó:   — |                      |¬¦  «        d         S r»   )Úlogisticr½   s       r)   rr   zLogistic._sample_formula  s   € Ø�|Š| ˆ|Ñ,Ô,¨RÔ0Ð0r*   N)rs   rt   ru   rv   r	   r   ry   r   r~   r|   r}   r5   r€   r   rÜ   r4   r9   r;   r=   r?   rA   rC   rG   rK   rT   r[   r^   rc   ri   r¹   rr   r/   r*   r)   r   r   Í   se  € € € € € ðð ð �¨3¨$°¨Ð5Ñ5Ô5€JØ)˜>¨#°jÈ'ÐRÑRÔRÐR€I�ØÐàŒU�W�R”W˜Q‘Z”ZÑ€Fð0ð 0ð 0ð(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ð ð ðLð Lð Lð9ð 9ð 9ðNð Nð Nð1ð 1ð 1ð 1ð 1r*   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©rá   Úb©TT©r   Ú	inclusive©gü©ñÒMbP?gÍÌÌÌÌÌì?r   rä   ©gš™™™™™ñ?g     @�@z\log(a))éýÿÿÿgš™™™™™¹¿r   Úlog_bz\log(b))çš™™™™™¹?r°   r   N©rá   rä   râ   rë   c                óD   •—  t          ¦   «         j        d||||dœ|¤Ž d S )Nrí   r/   r0   )r2   rá   rä   râ   rë   r'   r(   s         €r)   r1   z_LogUniform.__init__:  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 )Nrí   )r5   r“   r6   ÚupdateÚdict)r2   rá   rä   râ   rë   r'   s         r)   Ú_process_parametersz_LogUniform._process_parameters=  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/   )r2   r   râ   rë   r'   s        r)   r9   z_LogUniform._pdf_formulaH  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_oner5   Úrealr“   r‰   )r2   rb   râ   rë   r'   Út1Út2s          r)   rc   z_LogUniform._moment_raw_formulaN  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)rs   rt   ru   rv   r	   r   Ú	_a_domainÚ	_b_domainÚ_log_a_domainÚ_log_b_domainry   r   Ú_a_paramÚ_b_paramÚ_log_a_paramÚ_log_b_paramr|   Údefine_parametersr   r}   r~   r1   rò   r9   rc   r„   r…   s   @r)   rà   rà     sð  ø€ € € € € ðð ð �¨¨C¨Ð1Ñ1Ô1€IØ�¨¨c¨
Ð3Ñ3Ô3€IØ!�M¨c¨T°3¨KÐ8Ñ8Ô8€MØ!�M¨W°c¨NÐ;Ñ;Ô;€MØ�¨¸|ÐLÑLÔL€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*   rà   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   rá   rã   rå   ræ   rè   r   rä   ré   r   Nc                ó@   •—  t          ¦   «         j        d||dœ|¤Ž d S )Nrã   r/   r0   )r2   rá   rä   r'   r(   s       €r)   r1   zUniform.__init__p  ó-   ø€ Ø�‰ŒÔÐ,˜1 Ð,Ð, VÐ,Ð,Ð,Ð,Ð,r*   c                 óZ   — ||z
  }|                      t          |||¬¦  «        ¦  «         |S )N)rá   rä   Úab)rð   rñ   ©r2   rá   rä   r  r'   s        r)   rò   zUniform._process_parameterss  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"   )r5   ÚwhereÚisnanÚnanr6   ©r2   r   r  r'   s       r)   r4   zUniform._logpdf_formulax  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   )r5   r	  r
  r  r  s       r)   r9   zUniform._pdf_formula{  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 ©NrO   rP   ©r5   rU   r6   ©r2   r   rá   r  r'   s        r)   r;   zUniform._logcdf_formula~  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/   r  s        r)   r=   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 r  r  ©r2   r   rä   r  r'   s        r)   r?   zUniform._logccdf_formula…  r  r  c                ó   — ||z
  |z  S r"   r/   r  s        r)   rA   zUniform._ccdf_formula‰  r  r*   c                ó   — |||z  z   S r"   r/   )r2   Úprá   r  r'   s        r)   rC   zUniform._icdf_formulaŒ  ó   € Ø�2�a‘4‰xˆr*   c                ó   — |||z  z
  S r"   r/   )r2   r  rä   r  r'   s        r)   rG   zUniform._iccdf_formula�  r  r*   c                ó*   — t          j        |¦  «        S r"   rÓ   )r2   r  r'   s      r)   rK   zUniform._entropy_formula’  s   € ÝŒv�b‰zŒzÐr*   c                ó   — |d|z  z   S ©Nr   r/   r  s        r)   r^   zUniform._mode_formula•  ó   € Ø�3�r‘6‰zÐr*   c                ó   — |d|z  z   S r   r/   r  s        r)   r[   zUniform._median_formula˜  r!  r*   c                 ó.   — |dz   }||z  ||z  z
  ||z  z  S r  r/   )r2   rb   rá   rä   r  r'   Únp1s          r)   rc   zUniform._moment_raw_formula›  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/   )r2   rb   r  r'   s       r)   ri   zUniform._moment_central_formulaŸ  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)Nr¼   r/   r   r   )ÚuniformÚOverflowError)r2   rp   rq   rá   rä   r  r'   s          r)   rr   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)#rs   rt   ru   rv   r	   r   rù   rú   ry   r   rý   rþ   r|   r  r   r}   r~   r1   rò   r4   r9   r;   r=   r?   rA   rC   rG   rK   r^   r[   rc   ri   rƒ   rr   r„   r…   s   @r)   r   r   V  s  ø€ € € € € ð	ð 	ð �¨#¨¨s¨Ð4Ñ4Ô4€IØ�¨¨c¨
Ð3Ñ3Ô3€IØ�¨¸|ÐLÑLÔL€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*   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   ©FFræ   rá   )rì   é
   r   r   c                óh   — ||dz
  z  t          j        | ¦  «        z  t          j        |¦  «        z  S r  )r5   r“   r   Úgamma)r2   r   rá   r'   s       r)   r9   z_Gamma._pdf_formula¶  s.   € Ø�Q˜‘U‰|�bœf a R™jœjÑ(­7¬=¸Ñ+;Ô+;Ñ;Ð;r*   N)rs   rt   ru   r	   r   rù   ry   r   rý   r|   r   r}   r~   r9   r/   r*   r)   r+  r+  «  s–   € € € € € à�¨¨C¨Ð1Ñ1Ô1€IØ�¨!¨S¨¸^ÐLÑLÔL€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*   r+  c                   óL  ‡ — e Zd ZdZ edefd¬¦  «        Z edd¬¦  «        Z edd¬¦  «        Z	 e
ded	¬
¦  «        Z e
ded¬
¦  «        Z e
de	d¬
¦  «        Z eee¦  «        gZeZ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dge_        d„ Zg d¢e_        ˆ xZS )r   zÚBinomial 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,  ræ   )r   r   )r   rÙ   rå   rÙ   )r-  é   r   r  )g      Ð?g      è?r   )r   r-  c                ó@   •—  t          ¦   «         j        d||dœ|¤Ž d S )N©rÙ   r  r/   r0   )r2   rÙ   r  r'   r(   s       €r)   r1   zBinomial.__init__Ï  r  r*   c                ó.   — t          j        |||¦  «        S r"   )ÚscuÚ
_binom_pmf©r2   r   rÙ   r  r'   s        r)   Ú_pmf_formulazBinomial._pmf_formulaÒ  ó   € ÝŒ~˜a  AÑ&Ô&Ð&r*   c                óú   — t          j        |dz   ¦  «        t          j        |dz   ¦  «        t          j        ||z
  dz   ¦  «        z   z
  }|t          j        ||¦  «        z   t          j        ||z
  | ¦  «        z   S r  )r   ÚgammalnÚxlogyÚxlog1py)r2   r   rÙ   r  r'   Úcombilns         r)   Ú_logpmf_formulazBinomial._logpmf_formulaÕ  st   € õ
 ŒO˜A˜a™CÑ Ô ¥G¤O°A°a±CÑ$8Ô$8½7¼?È1ÈQÉ3ÈqÉ5Ñ;QÔ;QÑ$QÑRð 	ð �œ q¨!Ñ,Ô,Ñ,­w¬¸qÀ¹sÀQÀBÑ/GÔ/GÑGÐGr*   c                ó.   — t          j        |||¦  «        S r"   )r5  Ú
_binom_cdfr7  s        r)   r=   zBinomial._cdf_formulaÞ  r9  r*   c                ór   — |                       d||¬¦  «        }t          j        ||k     |||fd„ d„ ¦  «        S )Nr   r3  c                  óB   — t          j        t          j        | Ž ¦  «        S r"   )r5   r6   r5  rA  ©Úargss    r)   ú<lambda>z*Binomial._logcdf_formula.<locals>.<lambda>æ  s   € �"œ&¥¤°Ð!6Ñ7Ô7€ r*   c                  óD   — t          j        t          j        | Ž  ¦  «        S r"   )r5   rª   r5  Ú	_binom_sfrD  s    r)   rF  z*Binomial._logcdf_formula.<locals>.<lambda>ç  s   € �"œ(¥C¤M°4Ð$8Ð#8Ñ9Ô9€ r*   ©rC   ÚxpxÚapply_where©r2   r   rÙ   r  r'   Úmedians         r)   r;   zBinomial._logcdf_formulaá  sL   € ð ×#Ò# C¨1°Ð#Ñ2Ô2ˆÝŒ˜q 6šz¨A¨q°!¨9Ø7Ð7Ø9Ð9ñ
ô 
ð 	
r*   c                ó.   — t          j        |||¦  «        S r"   )r5  rH  r7  s        r)   rA   zBinomial._ccdf_formulaê  s   € ÝŒ}˜Q  1Ñ%Ô%Ð%r*   c                ór   — |                       d||¬¦  «        }t          j        ||k     |||fd„ d„ ¦  «        S )Nr   r3  c                  óD   — t          j        t          j        | Ž  ¦  «        S r"   )r5   rª   r5  rA  rD  s    r)   rF  z+Binomial._logccdf_formula.<locals>.<lambda>ð  s   € �"œ(¥C¤N°DÐ$9Ð#9Ñ:Ô:€ r*   c                  óB   — t          j        t          j        | Ž ¦  «        S r"   )r5   r6   r5  rH  rD  s    r)   rF  z+Binomial._logccdf_formula.<locals>.<lambda>ñ  s   € �"œ&¥¤°Ð!5Ñ6Ô6€ r*   rI  rL  s         r)   r?   zBinomial._logccdf_formulaí  sJ   € Ø×#Ò# C¨1°Ð#Ñ2Ô2ˆÝŒ˜q 6šz¨A¨q°!¨9Ø:Ð:Ø6Ð6ñ
ô 
ð 	
r*   c                ó.   — t          j        |||¦  «        S r"   )r5  Ú
_binom_ppfr7  s        r)   rC   zBinomial._icdf_formulaô  r9  r*   c                ó.   — t          j        |||¦  «        S r"   )r5  Ú
_binom_isfr7  s        r)   rG   zBinomial._iccdf_formula÷  r9  r*   c                ó€   — t          j        |dz   |z  ¦  «        }t          j        |dk    |dz
  |¦  «        }|d         S )Nr   r/   )r5   Úfloorr	  )r2   rÙ   r  r'   Úmodes        r)   r^   zBinomial._mode_formulaú  s=   € åŒx˜˜1™˜a™Ñ Ô ˆÝŒx˜˜Qš  q¡¨$Ñ/Ô/ˆØ�BŒxˆr*   c                óJ   — |dk    r||z  S |dk    r||z  d|z
  ||z  z   z  S d S r¨   r/   ©r2   rb   rÙ   r  r'   s        r)   rc   zBinomial._moment_raw_formula   s=   € à�AŠ:ˆ:Ø�Q‘3ˆJØ�AŠ:ˆ:Ø�Q‘3˜˜A™  !¡™Ñ$Ð$Øˆtr*   r   r    c                óÜ   — |dk    rt          j        |¦  «        S |dk    r||z  d|z
  z  S |dk    r||z  d|z
  z  dd|z  z
  z  S |dk    r ||z  d|z
  z  dd|z  dz
  |z  d|z
  z  z   z  S d S )Nr   r    r°   r±   é   )r5   rf   rZ  s        r)   ri   z Binomial._moment_central_formula	  s�   € à�AŠ:ˆ:Ý”= Ñ#Ô#Ð#Ø�AŠ:ˆ:Ø�Q‘3˜˜A™‘;ÐØ�AŠ:ˆ:Ø�Q‘3˜˜A™‘;  A a¡C¡Ñ(Ð(Ø�AŠ:ˆ:Ø�Q‘3˜˜A™‘;  Q q¡S¨1¡W¨a¡K°°Q±Ñ$7Ñ 7Ñ8Ð8Øˆtr*   )r   r    r°   r±   )rs   rt   ru   rv   r
   r   Ú	_n_domainr	   Ú	_p_domainry   r   Ú_n_paramÚ_p_paramr|   r   r}   r~   r1   r8  r?  r=   r;   rA   r?   rC   rG   r^   rc   rƒ   ri   r„   r…   s   @r)   r   r   º  s¡  ø€ € € € € ðð ð !Ð ¨A¨s¨8¸~ÐNÑNÔN€IØ�¨¸.ÐIÑIÔI€IØ!Ð!¨HÀÐMÑMÔM€Jàˆ~˜c¨)¸XÐFÑFÔF€HØˆ~˜c¨)¸\ÐJÑJÔJ€HØˆ~˜c¨*¸gÐFÑFÔF€Hà+Ð+¨H°hÑ?Ô?Ð@ÐØ€Ið-ð -ð -ð -ð -ð'ð 'ð 'ðHð Hð Hð'ð 'ð 'ð
ð 
ð 
ð&ð &ð &ð
ð 
ð 
ð'ð 'ð 'ð'ð 'ð 'ðð ð ðð ð ð #$ Q ÐÔð
ð 
ð 
ð &2 \ \ÐÔ"Ð"Ð"Ð"Ð"r*   r   )#ÚsysÚnumpyr5   r   Ú
scipy._libr   rJ  Úscipyr   Úscipy.specialr   r5  Ú(scipy.stats._distribution_infrastructurer   r   r	   r
   r   r   r   Ú__all__r   r‰   r%   r   rà   r   r+  r   Úmodulesrs   Ú__dict__Ú_moduleÚ	dist_namerv   r/   r*   r)   ú<module>rl     s‡  ðØ 
€
€
€
à Ð Ð Ð Ø Ð Ð Ð Ð Ð à -Ð -Ð -Ð -Ð -Ð -Ø Ð Ð Ð Ð Ð Ø (Ð (Ð (Ð (Ð (Ð (ð6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 6ð 8Ð
7Ð
7€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\C1ð C1ð C1ð C1ð C1Ð%ñ C1ô C1ð C1ðN?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Z2ð Z2ð Z2ð Z2ð Z2Ð#ñ Z2ô Z2ð Z2ð@ Œ+�hÔ
Ô
(€Øð Cð C€IØ!. ¨w°yÔ/AÑ!BÔ!B€GˆIÔÔÐðCð Cr*   