statsmodels.genmod.families.family.NegativeBinomial.loglike¶

NegativeBinomial.loglike(endog, mu, freq_weights=1.0, scale=1.0)[source]¶

The log-likelihood function in terms of the fitted mean response.

Parameters:

endog : array-like

Endogenous response variable

mu : array-like

The fitted mean response values

freq_weights : array-like

1d array of frequency weights. The default is 1.

scale : float

The scale parameter. The default is 1.

Returns:

llf : float

The value of the loglikelihood function evaluated at (endog,mu,freq_weights,scale) as defined below.

Notes

Defined as:

$llf = \sum_i freq\_weights_i * (Y_i * \log{(\alpha * e^{\eta_i} / (1 + \alpha * e^{\eta_i}))} - \log{(1 + \alpha * e^{\eta_i})}/ \alpha + Constant)$

where $Constant$ is defined as:

$Constant = \ln \Gamma{(Y_i + 1/ \alpha )} - \ln \Gamma(Y_i + 1) - \ln \Gamma{(1/ \alpha )}$