statsmodels.genmod.families.family.Poisson.loglike_obs

Poisson.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 Poisson distribution.

Parameters:
  • endog (array) – Usually the endogenous response variable.
  • mu (array) – 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

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