Џkh@?HddlZddlZddlmZddlmZddlmZmZm Z m Z m Z m Z m Z gdZGddeZdZGd d eZGd d eZGd deZGddeZGddeZej,ej0ZeD]Ze eeee_y)N)inf)special)ContinuousDistributionDiscreteDistribution _RealInterval_IntegerInterval_RealParameter_Parameterization _combine_docs)NormalUniformBinomialceZdZdZee efZedefZee efZe ddedZ e dd ed Z e d ed Z e e e gZe Zd ej"dej$zz Zej(dej$zdz Zd%fd Zdddfd ZdZdZdZdZdZdZdZdZdZ dZ!dZ"dZ#d Z$d!Z%d"Z&dd ge&_'d#Z(d$Z)xZ*S)&r aNormal 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)}  endpointsrmuz\mu)symboldomaintypicalsigmaz\sigma)?g?xrrrc P||t|tSt||SN)super__new__StandardNormal)clsrrkwargs __class__s Z/var/www/teggl/fontify/venv/lib/python3.12/site-packages/scipy/stats/_new_distributions.pyr!zNormal.__new__,s* :%-7?>2 2ws##?rrc *t|d||d|y)Nr*r __init__)selfrrr$r%s r&r.zNormal.__init__1s 6Be6v6r'c ftj|||z |z tj|z Sr)r"_logpdf_formulanplogr/rrrr$s r&r1zNormal._logpdf_formula4s*--dQVUNCbffUmSSr'c @tj|||z |z |z Sr)r" _pdf_formular4s r&r6zNormal._pdf_formula7s"**4!b&%@5HHr'c :tj|||z |z Sr)r"_logcdf_formular4s r&r8zNormal._logcdf_formula:s--dQVUNCCr'c :tj|||z |z Sr)r" _cdf_formular4s r&r:zNormal._cdf_formula=s**4!b&%@@r'c :tj|||z |z Sr)r"_logccdf_formular4s r&r<zNormal._logccdf_formula@s..ta"fe^DDr'c :tj|||z |z Sr)r" _ccdf_formular4s r&r>zNormal._ccdf_formulaCs++D1r65.AAr'c :tj|||z|zSr)r" _icdf_formular4s r&r@zNormal._icdf_formulaFs++D!4uQGG  0 0s 5BBc |Srr,rJs r&_median_formulazNormal._median_formula] r'c |Srr,rJs r& _mode_formulazNormal._mode_formula`rYr'c F|dk(rtj|S|dk(r|Sy)Nrr)r2 ones_liker/orderrrr$s r&_moment_raw_formulazNormal._moment_raw_formulacs' A:<<# # aZIr'c |dk(rtj|S|dzrtj|S||ztjt |dz dzS)NrrrT)exact)r2r] zeros_liker factorial2intr^s r&_moment_central_formulazNormal._moment_central_formulalsT A:<<# # QY==$ $%<'"4"4SZ!^4"PP Pr'c 0|j|||dS)N)locscalesizer,normal)r/ full_shaperngrrr$s r&_sample_formulazNormal._sample_formulauszzbJz?CCr')NN)+__name__ __module__ __qualname____doc__rr _mu_domain _sigma_domain _x_supportr _mu_param _sigma_param_x_paramr _parameterizations _variabler2sqrtpi_normalizationr3_log_normalizationr!r.r1r6r8r:r<r>r@rBrDrFrHrQrXr[r`ordersrfro __classcell__r%s@r&r r s> 3$5J!QH5M3$5JtVJ'.0I!')M*46Lc*gFH+I|DEIwrwwqw''N"%%*$  r7TIDAEBBECFJH#$QQDr'r c\tj||tjdzzgdS)Ny?rrO)rrSr2r})log_plog_qs r& _log_diffrys&   eU2558^41 ==r'ceZdZdZee efZededZeZ gZ de jde jzz Ze jde jzdz Ze j"dZe j"d Zd Zd Zd Zd ZdZdZdZdZdZdZdZdZdZ dZ!dZ"dZ#dZ$dZ%dZ&y)r"zStandard 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) rr)rrrr(r)c 0tj|fi|yr)rr.r/r$s r&r.zStandardNormal.__init__s''77r'c .|j|dzdz z SNr)rr/rr$s r&r1zStandardNormal._logpdf_formulas((1a46122r'c T|jtj|dz dz zSr)r~r2exprs r&r6zStandardNormal._pdf_formulas%""RVVQTE!G_44r'c ,tj|Srrlog_ndtrrs r&r8zStandardNormal._logcdf_formulas""r'c ,tj|Srrndtrrs r&r:zStandardNormal._cdf_formulas||Ar'c .tj| Srrrs r&r<zStandardNormal._logccdf_formulas##r'c .tj| Srrrs r&r>zStandardNormal._ccdf_formulas||QBr'c ,tj|Srrndtrirs r&r@zStandardNormal._icdf_formulas}}Qr'c ,tj|Srr ndtri_exprs r&rBzStandardNormal._ilogcdf_formulas  ##r'c .tj| Srrrs r&rDzStandardNormal._iccdf_formulas a   r'c .tj| Srrrs r&rFz StandardNormal._ilogccdf_formulas!!!$$$r'c Zdtjdtjzzdz SNrr)r2r3r}rs r&rHzStandardNormal._entropy_formulas"BFF1RUU7O#Q&&r'c tjtjdtjztjdz Sr)r2log1pr3r}rs r&rQz"StandardNormal._logentropy_formulas.xxqw(266!944r'c yNrr,rs r&rXzStandardNormal._median_formular'c yrr,rs r&r[zStandardNormal._mode_formularr'c 8ddddddd}|j|dS)Nrr)rrrrr)get)r/r_r$ raw_momentss r&r`z"StandardNormal._moment_raw_formulas%aA!: ud++r'c (|j|fi|Srr`r/r_r$s r&rfz&StandardNormal._moment_central_formula't''888r'c (|j|fi|Srrrs r&_moment_standardized_formulaz+StandardNormal._moment_standardized_formularr'c ,|j|dS)Nrjr,rk)r/rmrnr$s r&rozStandardNormal._sample_formulaszzzz*2..r'N)'rprqrrrsrrrvr ryr{rzr2r|r}r~r3rfloat64rrr.r1r6r8r:r<r>r@rBrDrFrHrQrXr[r`rfrror,r'r&r"r"}s3$5Jc*gFHIwrwwqw''N"%%* BB BJJrNE835#$  $!%'5,99/r'r"ceZdZdZedefZedefZee efZedefZ eddZ e ded Z e d ed Z e dd edZe dde dZe de d Zej#e e j#ee j#e e eeeee e gZeZdddddfd ZddZdZdZxZS) _LogUniformaLog-uniform distribution. The probability density function of the log-uniform distribution is: .. math:: f(x; a, b) = \frac{1} {x (\log(b) - \log(a))} If :math:`\log(X)` is a random variable that follows a uniform distribution between :math:`\log(a)` and :math:`\log(b)`, then :math:`X` is log-uniformly distributed with shape parameters :math:`a` and :math:`b`. rralog_arbTTr inclusivegMbP?g?rrg?g@@z\log(a))grlog_bz\log(b))皙?rrNrrrrc .t|d||||d|y)Nrr,r-)r/rrrrr$r%s r&r.z_LogUniform.__init__s F1eFvFr'c |tj|n|}|tj|n|}|tj|n|}|tj|n|}|jt |||||S)Nr)r2rr3updatedict)r/rrrrr$s r&_process_parametersz_LogUniform._process_parameterssjYBFF5MAYBFF5MA"]q "]q  dQ!5>? r'c ||z |zdzS)Nrr,)r/rrrr$s r&r6z_LogUniform._pdf_formulas!B&&r'c |dk(r |jS|j||z z |z }tjtjt ||z||z}||zSr)_oner2realrr)r/r_rrr$t1t2s r&r`z_LogUniform._moment_raw_formulasY A:99  YY%%- (5 0 WWRVVIeemUU]CD EBwr')NNNN)rprqrrrsrr _a_domain _b_domain _log_a_domain _log_b_domainrvr _a_param_b_param _log_a_param _log_b_paramrydefine_parametersr rzr{r.rr6r`rrs@r&rrs C1Ic 3I!cT3K8M!WcN;M|LJc)[IHc)ZHH!'*)6 LL!'*)6JLc*jIH )##L1  84+L,G+Hh?AI DDG' r'rcxeZdZdZee efZedefZeddZe dedZ e d ed Z e d edZ eje eje e ee e gZe Zd d dfd ZddZdZdZdZdZdZdZdZdZdZdZdZdZdZdge_ dZ!xZ"S)r zUniform distribution. The probability density function of the uniform distribution is: .. math:: f(x; a, b) = \frac{1} {b - a} rrrrrrrrrrNc *t|d||d|y)Nrr,r-)r/rrr$r%s r&r.zUniform.__init__( ,1,V,r'c J||z }|jt||||S)N)rrab)rrr/rrrr$s r&rzUniform._process_parameters+s% U dQ!+, r'c tjtj|tjtj| Sr)r2whereisnannanr3r/rrr$s r&r1zUniform._logpdf_formula0s+xx RVVbffRj[99r'c xtjtj|tjd|z SNr)r2rrrrs r&r6zUniform._pdf_formula3s%xx RVVQrT22r'c tjd5tj||z tj|z cdddS#1swYyxYwNrLrMr2rRr3r/rrrr$s r&r8zUniform._logcdf_formula6? 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