ó áp7]c@sødZddlZejeƒjZdefd„ƒYZeƒZ de _defd„ƒYZ e ƒZ de _e d d ƒZ d e _e d d ƒZ d e _defd„ƒYZeƒZde_defd„ƒYZeƒZde_dS(sP Variance functions for use with the link functions in statsmodels.family.links iÿÿÿÿNtVarianceFunctioncBs eZdZd„Zd„ZRS(s– 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 cCs%tj|ƒ}tj|jtjƒS(sÔ Default variance function Parameters ---------- mu : array-like mean parameters Returns ------- v : array ones(mu.shape) (tnptasarraytonestshapetfloat64(tselftmu((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyt__call__scCs tj|ƒS(s< Derivative of the variance function v'(mu) (Rt zeros_like(RR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pytderiv.s(t__name__t __module__t__doc__RR (((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyRs s~ The call method of constant returns a constant variance, i.e., a vector of ones. constant is an alias of VarianceFunction() tPowercBs,eZdZdd„Zd„Zd„ZRS(sv 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) gð?cCs ||_dS(N(tpower(RR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyt__init__WscCstjtj|ƒ|jƒS(så Power variance function Parameters ---------- mu : array-like mean parameters Returns ------- variance : array numpy.fabs(mu)**self.power (RRtfabs(RR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyRZscCsJ|jtj|ƒ|jd}tj|dkƒ}||cd9<|S(s_ Derivative of the variance function v'(mu) May be undefined at zero. iiiÿÿÿÿ(RRRt flatnonzero(RRtdertii((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyR js!(R R R RRR (((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyR>s  s> Returns np.fabs(mu) Notes ----- This is an alias of Power() Risa Returns np.fabs(mu)**2 Notes ----- This is an alias of statsmodels.family.links.Power(power=2) isa Returns np.fabs(mu)**3 Notes ----- This is an alias of statsmodels.family.links.Power(power=3) tBinomialcBs5eZdZdd„Zd„Zd„Zd„ZRS(sä 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) icCs ||_dS(N(tn(RR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyR¯scCstj|tdtƒS(Ni(Rtclipt FLOAT_EPS(Rtp((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyt_clean²scCs)|j||jƒ}|d||jS(sò Binomial variance function Parameters ---------- mu : array-like mean parameters Returns ------- variance : array variance = mu/n * (1 - mu/n) * self.n i(RR(RRR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyRµscCs dd|S(s< Derivative of the variance function v'(mu) ii((RR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyR Çs(R R R RRRR (((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyR‘s    sY The binomial variance function for n = 1 Notes ----- This is an alias of Binomial(n=1) tNegativeBinomialcBs5eZdZdd„Zd„Zd„Zd„ZRS(s  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) gð?cCs ||_dS(N(talpha(RR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyRôscCstj|ttjƒS(N(RRRtinf(RR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyR÷scCs"|j|ƒ}||j|dS(sò Negative binomial variance function Parameters ---------- mu : array-like mean parameters Returns ------- variance : array variance = mu + alpha*mu**2 i(RR(RRR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyRúscCs"|j|ƒ}dd|j|S(sH Derivative of the negative binomial variance function. ii(RR(RRR((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyR s(R R R RRRR (((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyRØs    sb Negative Binomial variance function. Notes ----- This is an alias of NegativeBinomial(alpha=1.) (R tnumpyRtfinfotfloattepsRtobjectRtconstantRRt mu_squaredtmu_cubedRtbinaryRtnbinom(((sClib/python2.7/site-packages/statsmodels/genmod/families/varfuncs.pyts$ -  9    =  <