statsmodels.genmod.families.family.NegativeBinomial

class statsmodels.genmod.families.family.NegativeBinomial(link=<class 'statsmodels.genmod.families.links.log'>, alpha=1.0)[source]

Negative Binomial exponential family.

Parameters:

link : a link instance, optional

The default link for the negative binomial family is the log link. Available links are log, cloglog, identity, nbinom and power. See statsmodels.family.links for more information.

alpha : float, optional

The ancillary parameter for the negative binomial distribution. For now alpha is assumed to be nonstochastic. The default value is 1. Permissible values are usually assumed to be between .01 and 2.

See also

statsmodels.genmod.families.family.Family, Link Functions

Notes

Power link functions are not yet supported.

Parameterization for y=0,1,2,\ldots is

f(y) = \frac{\Gamma(y+\frac{1}{\alpha})}{y!\Gamma(\frac{1}{\alpha})} \left(\frac{1}{1+\alpha\mu}\right)^{\frac{1}{\alpha}} \left(\frac{\alpha\mu}{1+\alpha\mu}\right)^y

with E[Y]=\mu\, and Var[Y]=\mu+\alpha\mu^2.

Attributes

NegativeBinomial.link (a link instance) The link function of the negative binomial instance
NegativeBinomial.variance (varfunc instance) variance is an instance of statsmodels.family.varfuncs.nbinom

Methods

deviance(endog, mu[, freq_weights, scale]) Returns the value of the deviance function.
fitted(lin_pred) Fitted values based on linear predictors lin_pred.
loglike(endog, mu[, freq_weights, scale]) The log-likelihood function in terms of the fitted mean response.
predict(mu) Linear predictors based on given mu values.
resid_anscombe(endog, mu) The Anscombe residuals for the negative binomial family
resid_dev(endog, mu[, scale]) Negative Binomial Deviance Residual
starting_mu(y) Starting value for mu in the IRLS algorithm.
variance
weights(mu) Weights for IRLS steps

Methods

deviance(endog, mu[, freq_weights, scale]) Returns the value of the deviance function.
fitted(lin_pred) Fitted values based on linear predictors lin_pred.
loglike(endog, mu[, freq_weights, scale]) The log-likelihood function in terms of the fitted mean response.
predict(mu) Linear predictors based on given mu values.
resid_anscombe(endog, mu) The Anscombe residuals for the negative binomial family
resid_dev(endog, mu[, scale]) Negative Binomial Deviance Residual
starting_mu(y) Starting value for mu in the IRLS algorithm.
weights(mu) Weights for IRLS steps