Yh@?nddlZddlZddlmZddlmZddlmZmZm Z m Z m Z m Z m Z gdZGddeZdZGd d eZGd d eZGd deZGddeZGddeZejejZeD]Ze eeee_dS)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 ejdejzz Zejdejzdz Zd&fd Zdddfd ZdZdZdZdZdZdZdZdZdZ dZ!dZ"d Z#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?xrrrNc |(|&ttSt|SN)super__new__StandardNormal)clsrrkwargs __class__s p/var/www/tools.fuzzalab.pt/emblema-extractor/venv/lib/python3.11/site-packages/scipy/stats/_new_distributions.pyr!zNormal.__new__,s8 :%-77??>22 2wws###?rrc @tjd||d|dS)Nr*r __init__)selfrrr$r%s r&r.zNormal.__init__1s-6Be66v66666r'c nt|||z |z tj|z Sr)r"_logpdf_formulanplogr/rrrr$s r&r1zNormal._logpdf_formula4s---dQVUNCCbfUmmSSr'c Jt|||z |z |z Sr)r" _pdf_formular4s r&r6zNormal._pdf_formula7s%**4!b&%@@5HHr'c Dt|||z |z Sr)r"_logcdf_formular4s r&r8zNormal._logcdf_formula:s --dQVUNCCCr'c Dt|||z |z Sr)r" _cdf_formular4s r&r:zNormal._cdf_formula=s **4!b&%@@@r'c Dt|||z |z Sr)r"_logccdf_formular4s r&r<zNormal._logccdf_formula@s ..ta"fe^DDDr'c Dt|||z |z Sr)r" _ccdf_formular4s r&r>zNormal._ccdf_formulaCs ++D1r65.AAAr'c Dt|||z|zSr)r" _icdf_formular4s r&r@zNormal._icdf_formulaFs"++D!44u!>QGGGGs7A33A7:A7c |Srr,rJs r&_median_formulazNormal._median_formula] r'c |Srr,rJs r& _mode_formulazNormal._mode_formula`rYr'c J|dkrtj|S|dkr|SdS)Nrr)r2 ones_liker/orderrrr$s r&_moment_raw_formulazNormal._moment_raw_formulacs. A::<## # aZZI4r'c |dkrtj|S|dzrtj|S||ztjt |dz dzS)NrrrT)exact)r2r] zeros_liker factorial2intr^s r&_moment_central_formulazNormal._moment_central_formulalsc A::<## # QY Q=$$ $%<'"4SZZ!^4"P"P"PP Pr'c >||||dS)N)locscalesizer,normal)r/ full_shaperngrrr$s r&_sample_formulazNormal._sample_formulauszzbJz??CCr')NN)+__name__ __module__ __qualname____doc__rr _mu_domain _sigma_domain _x_supportr _mu_param _sigma_param_x_paramr _parameterizations _variabler2sqrtpi_normalizationr3_log_normalizationr!r.r1r6r8r:r<r>r@rBrDrFrHrQrXr[r`ordersrfro __classcell__r%s@r&r r s  3$555J!MQH555M3$555JtVJ'.000I!>')M*4666L~c*gFFFH++I|DDEIwrwqw'''N"%*$$$$$$  r7777777TTTIIIDDDAAAEEEBBBBBBEEECCCFFFJJJHHH#$QQQQDDDDDDDr'r cRtj||tjdzzgdS)Ny?rrO)rrSr2r})log_plog_qs r& _log_diffrys'  eU258^41 = = ==r'creZdZdZee efZededZeZ gZ de j de j zz Ze jde j zdz Ze jdZe jd Zd Zd Zd Zd ZdZdZdZdZdZdZdZdZdZ dZ!dZ"dZ#dZ$dZ%dZ&dS)r"zStandard normal distribution. The probability density function of the standard normal distribution is: .. math:: f(x) = \frac{1}{\sqrt{2 \pi}} \exp \left( -\frac{1}{2} x^2 \right) rr)rrrr(r)c *tj|fi|dSr)rr.r/r$s r&r.zStandardNormal.__init__s!'7777777r'c $|j|dzdz z SNr)rr/rr$s r&r1zStandardNormal._logpdf_formulas(1a46122r'c H|jtj|dz dz zSr)r~r2exprs r&r6zStandardNormal._pdf_formulas""RVQTE!G__44r'c *tj|Srrlog_ndtrrs r&r8zStandardNormal._logcdf_formulas"""r'c *tj|Srrndtrrs r&r:zStandardNormal._cdf_formulas|Ar'c ,tj| Srrrs r&r<zStandardNormal._logccdf_formulas###r'c ,tj| Srrrs r&r>zStandardNormal._ccdf_formulas|QBr'c *tj|Srrndtrirs r&r@zStandardNormal._icdf_formulas}Qr'c *tj|Srr ndtri_exprs r&rBzStandardNormal._ilogcdf_formulas ###r'c ,tj| Srrrs r&rDzStandardNormal._iccdf_formulas a    r'c ,tj| Srrrs r&rFz StandardNormal._ilogccdf_formulas!!$$$$r'c Pdtjdtjzzdz SNrr)r2r3r}rs r&rHzStandardNormal._entropy_formulas BF1RU7OO#Q&&r'c tjtjdtjztjdz Sr)r2log1pr3r}rs r&rQz"StandardNormal._logentropy_formulas-xqw((26!9944r'c dSNrr,rs r&rXzStandardNormal._median_formulaqr'c dSrr,rs r&r[zStandardNormal._mode_formularr'c @ddddddd}||dS)Nrr)rrrrr)get)r/r_r$ raw_momentss r&r`z"StandardNormal._moment_raw_formulas+aA!:: ud+++r'c |j|fi|Srr`r/r_r$s r&rfz&StandardNormal._moment_central_formula't'88888r'c |j|fi|Srrrs r&_moment_standardized_formulaz+StandardNormal._moment_standardized_formularr'c :||dS)Nrjr,rk)r/rmrnr$s r&rozStandardNormal._sample_formulaszzzz**2..r'N)'rprqrrrsrrrvr ryr{rzr2r|r}r~r3rfloat64rrr.r1r6r8r:r<r>r@rBrDrFrHrQrXr[r`rfrror,r'r&r"r"}s3$555J~c*gFFFHIwrwqw'''N"%* BB BJrNNE888333555###$$$      $$$!!!%%%'''555,,,999999/////r'r"ceZdZdZedefZedefZee efZedefZ eddZ e ded Z e d ed Z e dd edZe dde dZe de d Zee e ee 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 Dtjd||||d|dS)Nrr,r-)r/rrrrr$r%s r&r.z_LogUniform.__init__s1F1eFFvFFFFFr'c |tj|n|}|tj|n|}|tj|n|}|tj|n|}|t |||||S)Nr)r2rr3updatedict)r/rrrrr$s r&_process_parametersz_LogUniform._process_parameterss~YBF5MMMAYBF5MMMA"]q "]q  dQ!5>>>??? r'c ||z |zdzS)Nrr,)r/rrrr$s r&r6z_LogUniform._pdf_formulas!B&&r'c |dkr|jS|j||z z |z }tjtjt ||z||z}||zSr)_oner2realrr)r/r_rrr$t1t2s r&r`z_LogUniform._moment_raw_formulas\ A::9  Y%%- (5 0 WRVIeemUU]CCDD E 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   C111I c 333I!McT3K888M!MWcN;;;M|LLLJ~c)[IIIH~c)ZHHHH!>'*)6 LLLL!>'*)6JJJL~c*jIIIH )))##L111  8444++L,GG++Hh??AI DDGGGGGGG''' r'rceZdZdZee efZedefZeddZe dedZ e d ed Z e d edZ e e e e 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 @tjd||d|dS)Nrr,r-)r/rrr$r%s r&r.zUniform.__init__(-,1,,V,,,,,r'c Z||z }|t||||S)N)rrab)rrr/rrrr$s r&rzUniform._process_parameters+s1 U dQ!+++,,, r'c tjtj|tjtj| Sr)r2whereisnannanr3r/rrr$s r&r1zUniform._logpdf_formula0s*x RVbfRjj[999r'c ltjtj|tjd|z SNr)r2rrrrs r&r6zUniform._pdf_formula3s$x RVQrT222r'c tjd5tj||z tj|z cdddS#1swxYwYdSNrLrMr2rRr3r/rrrr$s r&r8zUniform._logcdf_formula6 [ ) ) ) . .6!a%==26"::- . . . . . . . . . . . . . . . . . .,AAAc ||z |z Srr,rs r&r:zUniform._cdf_formula:A|r'c tjd5tj||z tj|z cdddS#1swxYwYdSrrr/rrrr$s r&r<zUniform._logccdf_formula=rrc ||z |z Srr,rs r&r>zUniform._ccdf_formulaArr'c |||zzSrr,)r/prrr$s r&r@zUniform._icdf_formulaD2a4xr'c |||zz Srr,)r/rrrr$s r&rDzUniform._iccdf_formulaGrr'c *tj|Sr)r2r3)r/rr$s r&rHzUniform._entropy_formulaJsvbzzr'c |d|zzSNrr,rs r&r[zUniform._mode_formulaM3r6zr'c |d|zzSrr,rs r&rXzUniform._median_formulaPrr'c .|dz}||z||zz ||zz Srr,)r/r_rrrr$np1s r&r`zUniform._moment_raw_formulaSs&ai3CC"H--r'c "|dkr|dzdz ndS)Nr r,)r/r_rr$s r&rfzUniform._moment_central_formulaWs A::r1uRxx4/r'rc ||||dS#t$r!|dd||z|zcYSwxYw)Nrr,rr)uniform OverflowError)r/rmrnrrrr$s r&rozUniform._sample_formula\sg =;;q!*;55b9 9 = = =;;q!*;55b81< < < < =s (A  A )NNN)#rprqrrrsrrrrrvr rrryrr rzr{r.rr1r6r8r:r<r>r@rDrHr[rXr`rfrrorrs@r&r r s   #s 444I c 333I|LLLJ~c)[IIIH~c)ZHHHH~c*jIIIH )))  8444++Hh??@I D------- :::333.........000'(S"=======r'r ceZdZedefZedefdZededZededZ e egZ e Z d Z d S) _GammarrFFrr)r rrc h||dz ztj| ztj|z Sr)r2rrgamma)r/rrr$s r&r6z_Gamma._pdf_formulans.QU|bfaRjj(7=+;+;;;r'N)rprqrrrrrrvr rryr rzr{r6r,r'r&rrcs C111I!S^LLLJ~c)YGGGH~c*iHHHH++H556I<<<<zBinomial._ccdf_formulas((Aq111r'c Dtj|||Sr)rr  _binom_ppfrs r&r@zBinomial._icdf_formularr'c Dtj|||Sr)rr  _binom_isfrs r&rDzBinomial._iccdf_formularr'c tj|dz|z}tj|dk|dz |}|dS)Nrr,)r2floorr)r/r rr$modes r&r[zBinomial._mode_formulas=x1a  xQq$//Bxr'c J|dkr||zS|dkr||zd|z ||zzzSdSrr,r/r_r rr$s r&r`zBinomial._moment_raw_formulas= A::Q3J A::Q3A! $ $tr'rrc |dkrtj|S|dkr ||zd|z zS|dkr||zd|z zdd|zz zS|dkr ||zd|z zdd|zdz |zd|z zzzSdS)Nrrrr)r2rcr$s r&rfz Binomial._moment_central_formulas A::=## # A::Q3A;  A::Q3A;AaC( ( A::Q3A;QqS1WaKQ$7 78 8tr')rrrr)rprqrrrsrr _n_domainr _p_domainrvr _n_param_p_paramryr rzr{r.rrr:r>r@rDr[r`rrfrrs@r&rrrs! 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