!gHdZddlZejej ZGddZeZde_GddZ e Z de _e d Z d e _e d Z d e _GddZ e Zde_GddZeZde_y)zP Variance functions for use with the link functions in statsmodels.family.links NceZdZdZdZdZy)VarianceFunctiona Relates the variance of a random variable to its mean. Defaults to 1. Methods ------- call Returns an array of ones that is the same shape as `mu` Notes ----- After a variance function is initialized, its call method can be used. Alias for VarianceFunction: constant = VarianceFunction() See Also -------- statsmodels.genmod.families.family ctj|}tj|jtjS)z Default variance function Parameters ---------- mu : array_like mean parameters Returns ------- v : ndarray ones(mu.shape) )npasarrayonesshapefloat64selfmus a/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/genmod/families/varfuncs.py__call__zVarianceFunction.__call__s*ZZ^wwrxx,,c,tj|S)< Derivative of the variance function v'(mu) )r zeros_liker s rderivzVarianceFunction.deriv.s}}R  rN)__name__ __module__ __qualname____doc__rrrrrrs(-"!rrz~ The call method of constant returns a constant variance, i.e., a vector of ones. constant is an alias of VarianceFunction() c$eZdZdZddZdZdZy)Powerav Power variance function Parameters ---------- power : float exponent used in power variance function Methods ------- call Returns the power variance Notes ----- Formulas V(mu) = numpy.fabs(mu)**power Aliases for Power: mu = Power() mu_squared = Power(power=2) mu_cubed = Power(power=3) c||_yNpower)r rs r__init__zPower.__init__W  rchtjtj||jS)z Power variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray numpy.fabs(mu)**self.power )rrfabsr s rrzPower.__call__Zs!xx TZZ00rc|jtj||jdz zz}tj|dk}||xxdzcc<|S)z_ Derivative of the variance function v'(mu) May be undefined at zero. r)rrr# flatnonzero)r r deriis rrz Power.derivjsKjj2772;4::>:: ^^BF # B2  rNg?)rrrrr rrrrrrr>s01 rrz> Returns np.fabs(mu) Notes ----- This is an alias of Power() rza Returns np.fabs(mu)**2 Notes ----- This is an alias of statsmodels.family.links.Power(power=2) za Returns np.fabs(mu)**3 Notes ----- This is an alias of statsmodels.family.links.Power(power=3) c*eZdZdZddZdZdZdZy)Binomiala Binomial variance function Parameters ---------- n : int, optional The number of trials for a binomial variable. The default is 1 for p in (0,1) Methods ------- call Returns the binomial variance Notes ----- Formulas : V(mu) = p * (1 - p) * n where p = mu / n Alias for Binomial: binary = Binomial() A private method _clean trims the data by machine epsilon so that p is in (0,1) c||_yr)n)r r0s rr zBinomial.__init__s rcFtj|tdtz S)Nr%)rclip FLOAT_EPSr ps r_cleanzBinomial._cleanswwq)Q]33rch|j||jz }|d|z z|jzS)z Binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu/n * (1 - mu/n) * self.n r%)r6r0r r r5s rrzBinomial.__call__s1 KKTVV $AE{TVV##rcdd|zz S)rr%r+rr s rrzBinomial.derivs1R4xrN)r%rrrrr r6rrrrrr.r.s:4$$rr.zY The binomial variance function for n = 1 Notes ----- This is an alias of Binomial(n=1) c*eZdZdZddZdZdZdZy)NegativeBinomiala  Negative binomial variance function Parameters ---------- alpha : float The ancillary parameter for the negative binomial variance function. `alpha` is assumed to be nonstochastic. The default is 1. Methods ------- call Returns the negative binomial variance Notes ----- Formulas : V(mu) = mu + alpha*mu**2 Alias for NegativeBinomial: nbinom = NegativeBinomial() A private method _clean trims the data by machine epsilon so that p is in (0,inf) c||_yr)alpha)r r>s rr zNegativeBinomial.__init__r!rcTtj|ttjSr)rr2r3infr4s rr6zNegativeBinomial._cleanswwq)RVV,,rcN|j|}||j|dzzzS)z Negative binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu + alpha*mu**2 r+r6r>r8s rrzNegativeBinomial.__call__s( KKO4::ad?""rcN|j|}dd|jz|zzS)zH Derivative of the negative binomial variance function. r%r+rBr8s rrzNegativeBinomial.deriv s) KKO1tzz>A%%%rNr*r:rrrr<r<s6-#"&rr<zb Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) )rnumpyrfinfofloatepsr3rconstantrr mu_squaredmu_cubedr.binaryr<nbinomrrrrMs BHHUO   *!*!Z  66r W ^   q>::z 9&9&x  r