M/PhxdZddlZejejZGddZeZde_GddZ e Z de _e d Z d e _e d Z d e _GddZ e Zde_GddZeZde_dS)zP Variance functions for use with the link functions in statsmodels.family.links NceZdZdZdZdZdS)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 crtj|}tj|jtjS)z Default variance function Parameters ---------- mu : array_like mean parameters Returns ------- v : ndarray ones(mu.shape) )npasarrayonesshapefloat64selfmus d/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/genmod/families/varfuncs.py__call__zVarianceFunction.__call__s'Z^^wrx,,,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&eZdZdZddZdZdZdS)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||_dSNpower)r r s r__init__zPower.__init__W  rcZtjtj||jS)z Power variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray numpy.fabs(mu)**self.power )rr fabsr s rrzPower.__call__Zs x TZ000rc|jtj||jdz zz}tj|dk}||xxdzcc<|S)z_ Derivative of the variance function v'(mu) May be undefined at zero. r)r rr$ flatnonzero)r r deriis rrz Power.derivjsPj272;;4:>:: ^BF # # B2  rNr)rrrrr!rrrrrrr>sP0111     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,eZdZdZddZdZdZdZdS) 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) r&c||_dSr)n)r r1s rr!zBinomial.__init__s rcHtj|tdtz S)Nr&)rclip FLOAT_EPSr ps r_cleanzBinomial._cleanswq)Q]333rc\|||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&)r7r1r r r6s rrzBinomial.__call__s0 KKTV $ $AE{TV##rcdd|zz S)rr&r,rr s rrzBinomial.derivs1R4xrN)r&rrrrr!r7rrrrrr/r/s_:444$$$$rr/zY The binomial variance function for n = 1 Notes ----- This is an alias of Binomial(n=1) c,eZdZdZddZdZdZdZdS) 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) rc||_dSr)alpha)r r?s rr!zNegativeBinomial.__init__r"rcLtj|ttjSr)rr3r4infr5s rr7zNegativeBinomial._cleanswq)RV,,,rcL||}||j|dzzzS)z Negative binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu + alpha*mu**2 r,r7r?r9s rrzNegativeBinomial.__call__s( KKOO4:ad?""rcL||}dd|jz|zzS)zH Derivative of the negative binomial variance function. r&r,rCr9s rrzNegativeBinomial.deriv s) KKOO1tz>A%%%rNr+r;rrrr=r=s_6---###"&&&&&rr=zb Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) )rnumpyrfinfofloatepsr4rconstantrr mu_squaredmu_cubedr/binaryr=nbinomrrrrNsl BHUOO  *!*!*!*!*!*!*!*!Z    66666666r UWW U^^^   5q>>>::::::::z 9&9&9&9&9&9&9&9&x    r