class, alpha=1.0)[source]

Negative Binomial exponential family.

  • 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.genmod.families.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.

a link instance – The link function of the negative binomial instance


varfunc instancevariance is an instance of statsmodels.genmod.families.varfuncs.nbinom


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 \(Var[Y]=\mu+\alpha\mu^2\).


deviance(endog, mu[, var_weights, …]) The deviance function evaluated at (endog, mu, var_weights, freq_weights, scale) for the distribution.
fitted(lin_pred) Fitted values based on linear predictors lin_pred.
loglike(endog, mu[, var_weights, …]) The log-likelihood function in terms of the fitted mean response.
loglike_obs(endog, mu[, var_weights, scale]) The log-likelihood function for each observation in terms of the fitted mean response for the Negative Binomial distribution.
predict(mu) Linear predictors based on given mu values.
resid_anscombe(endog, mu[, var_weights, scale]) The Anscombe residuals
resid_dev(endog, mu[, var_weights, scale]) The deviance residuals
starting_mu(y) Starting value for mu in the IRLS algorithm.
weights(mu) Weights for IRLS steps