statsmodels.genmod.families.family.NegativeBinomial

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

Negative Binomial exponential family.

Parameters

linka 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.

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.

See also

statsmodels.genmod.families.family.Family

Parent class for all links.

Link Functions

Further details on links.

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.linka link instance

The link function of the negative binomial instance

NegativeBinomial.variancevarfunc instance

variance is an instance of statsmodels.genmod.families.varfuncs.nbinom

Methods

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.
variance
weights(mu)	Weights for IRLS steps

Methods

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

Properties

link	Link function for family
links
safe_links
valid
variance