# statsmodels.genmod.families.family.NegativeBinomial¶

class statsmodels.genmod.families.family.NegativeBinomial(link=None, alpha=1.0)[source]

Negative Binomial exponential family.

Parameters

alphafloat, 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.

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
variance is an instance of statsmodels.genmod.families.varfuncs.nbinom
 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. 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 value for mu in the IRLS algorithm. variance Weights for IRLS steps