statsmodels.genmod.families.family.NegativeBinomial¶
-
class
statsmodels.genmod.families.family.
NegativeBinomial
(link=None, 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.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.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.link (a link instance) The link function of the negative binomial instance NegativeBinomial.variance (varfunc instance) variance
is an instance of statsmodels.genmod.families.varfuncs.nbinomMethods
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