U md@sdZddlZeejZGdddZeZde_GdddZ e Z de _e d d Z d e _e d d Z d e _GdddZ e Zde_GdddZeZde_dS)zP Variance functions for use with the link functions in statsmodels.family.links Nc@s eZdZdZddZddZdS)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 cCst|}t|jtjS)z Default variance function Parameters ---------- mu : array_like mean parameters Returns ------- v : ndarray ones(mu.shape) )npZasarrayZonesshapeZfloat64selfmur]/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/genmod/families/varfuncs.py__call__s zVarianceFunction.__call__cCs t|S)< Derivative of the variance function v'(mu) )rZ zeros_likerrrr deriv.szVarianceFunction.derivN)__name__ __module__ __qualname____doc__r r rrrr rsrz~ The call method of constant returns a constant variance, i.e., a vector of ones. constant is an alias of VarianceFunction() c@s*eZdZdZd ddZddZddZd S) 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) ?cCs ||_dSNpower)rrrrr __init__WszPower.__init__cCstt||jS)z Power variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray numpy.fabs(mu)**self.power )rrfabsrrrr r ZszPower.__call__cCs<|jt||jd}t|dk}||d9<|S)z_ Derivative of the variance function v'(mu) May be undefined at zero. r)rrrZ flatnonzero)rrZderiirrr r jsz Power.derivN)r)r rrrrr r rrrr r>s rz> 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@s2eZdZdZd ddZddZddZd d Zd S) 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) rcCs ||_dSr)n)rrrrr rszBinomial.__init__cCst|tdtS)Nr)rclip FLOAT_EPSrprrr _cleanszBinomial._cleancCs"|||j}|d||jS)z Binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu/n * (1 - mu/n) * self.n r)r#rrrr"rrr r szBinomial.__call__cCs dd|S)r rrrrrrr r szBinomial.derivN)rr rrrrr#r r rrrr rs  rzY The binomial variance function for n = 1 Notes ----- This is an alias of Binomial(n=1) c@s2eZdZdZd ddZddZddZd d Zd S) 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) rcCs ||_dSr)alpha)rr'rrr rszNegativeBinomial.__init__cCst|ttjSr)rrr infr!rrr r#szNegativeBinomial._cleancCs||}||j|dS)z Negative binomial variance function Parameters ---------- mu : array_like mean parameters Returns ------- variance : ndarray variance = mu + alpha*mu**2 rr#r'r$rrr r s zNegativeBinomial.__call__cCs||}dd|j|S)zH Derivative of the negative binomial variance function. rrr)r$rrr r s zNegativeBinomial.derivN)rr%rrrr r&s  r&zb Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) )rnumpyrZfinfofloatZepsr rZconstantrrZ mu_squaredZmu_cubedrbinaryr&Znbinomrrrr s$ -9   = <