statsmodels.genmod.families.family.Poisson.loglike_obs

Poisson.loglike_obs(endog, mu, var_weights=1.0, scale=1.0)

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

Parameters:

endogndarray

Usually the endogenous response variable.

mundarray

Usually but not always the fitted mean response variable.

var_weightsarray_like

1d array of variance (analytic) weights. The default is 1.

scalefloat

The scale parameter. The default is 1.

Returns:

ll_ifloat

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

Notes

\[ll_i = var\_weights_i / scale * (endog_i * \ln(\mu_i) - \mu_i - \ln \Gamma(endog_i + 1))\]