B Zk@sdZdZddlZeejZGdddeZ e Z de _GdddeZ e Z d e _e d d Z d e _e d d Zde_GdddeZeZde_GdddeZeZde_dS)zP Variance functions for use with the link functions in statsmodels.family.links ZrestructuredtextNc@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 : array ones(mu.shape) )npZasarrayZonesshapeZfloat64)selfmurClib/python3.7/site-packages/statsmodels/genmod/families/varfuncs.py__call__s zVarianceFunction.__call__cCs t|S)z< Derivative of the variance function v'(mu) )rZ zeros_like)rrrrrderiv0szVarianceFunction.derivN)__name__ __module__ __qualname____doc__r r rrrrr srz~ 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) Powera Power variance function Parameters ---------- power : float exponent used in power variance function Methods ------- call Returns the power variance Formulas -------- V(mu) = numpy.fabs(mu)**power Notes ----- Aliases for Power: mu = Power() mu_squared = Power(power=2) mu_cubed = Power(power=3) ?cCs ||_dS)N)power)rrrrr__init__XszPower.__init__cCstt||jS)z Power variance function Parameters ---------- mu : array-like mean parameters Returns ------- variance : array numpy.fabs(mu)**self.power )rrfabs)rrrrrr [szPower.__call__cCs<|jt||jd}t|dk}||d9<|S)z_ Derivative of the variance function v'(mu) May be undefined at zero. r)rrrZ flatnonzero)rrZderZiirrrr ksz Power.derivN)r)r r r rrr r rrrrr>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 Formulas -------- V(mu) = p * (1 - p) * n where p = mu / n Notes ----- Alias for Binomial: binary = Binomial() A private method _clean trims the data by machine epsilon so that p is in (0,1) rcCs ||_dS)N)n)rrrrrrszBinomial.__init__cCst|tdtS)Nr)rclip FLOAT_EPS)rprrr_cleanszBinomial._cleancCs"|||j}|d||jS)z Binomial variance function Parameters ----------- mu : array-like mean parameters Returns ------- variance : array variance = mu/n * (1 - mu/n) * self.n r)rr)rrrrrrr szBinomial.__call__cCs dd|S)z< Derivative of the variance function v'(mu) rrr)rrrrrr szBinomial.derivN)r)r r r rrrr r rrrrrs  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 Formulas -------- V(mu) = mu + alpha*mu**2 Notes ----- Alias for NegativeBinomial: nbinom = NegativeBinomial() A private method _clean trims the data by machine epsilon so that p is in (0,inf) ?cCs ||_dS)N)alpha)rr rrrrszNegativeBinomial.__init__cCst|ttjS)N)rrrinf)rrrrrrszNegativeBinomial._cleancCs||}||j|dS)z Negative binomial variance function Parameters ---------- mu : array-like mean parameters Returns ------- variance : array variance = mu + alpha*mu**2 r)rr )rrrrrrr s zNegativeBinomial.__call__cCs||}dd|j|S)zH Derivative of the negative binomial variance function. rr)rr )rrrrrrr s zNegativeBinomial.derivN)r)r r r rrrr r rrrrrs  rzb Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) )rZ __docformat__ZnumpyrZfinfofloatZepsrobjectrZconstantrrZ mu_squaredZmu_cubedrZbinaryrZnbinomrrrrs& -:  =;