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.
- link
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.nbinom
- NegativeBinomial.link
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 function for family