statsmodels.genmod.families.family.Gamma.loglike_obs

Gamma.loglike_obs(endog, mu, var_weights=1.0, scale=1.0)[source]

The log-likelihood function for each observation in terms of the fitted mean response for the Gamma distribution.

Parameters:

  • endog (ndarray) – Usually the endogenous response variable.

  • mu (ndarray) – Usually but not always the fitted mean response variable.

  • var_weights (array_like) – 1d array of variance (analytic) weights. The default is 1.

  • scale (float) – The scale parameter. The default is 1.

Returns:

ll_i – The value of the loglikelihood evaluated at (endog, mu, var_weights, scale) as defined below.

Return type:

float

Notes

\[ll_i = var\_weights_i / scale * (\ln(var\_weights_i * endog_i / (scale * \mu_i)) - (var\_weights_i * endog_i) / (scale * \mu_i)) - \ln \Gamma(var\_weights_i / scale) - \ln(\mu_i)\]