statsmodels.genmod.families.family.Gamma.loglike¶

Gamma.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

Fitted mean response variable

freq_weights : array-like

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

scale : float, optional

The default is 1.

Returns:

llf : float

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

Notes

$llf = -1 / scale * \sum_i *(Y_i / \mu_i+ \log(\mu_i)+ (scale -1) * \log(Y) + \log(scale) + scale * \ln \Gamma(1 / scale))$