statsmodels.discrete.discrete_model.GeneralizedPoisson.loglikeobs¶
- GeneralizedPoisson.loglikeobs(params)[source]¶
Loglikelihood for observations of Generalized Poisson model
- Parameters:
- paramsarray_like
The parameters of the model.
- Returns:
- loglike
ndarray The log likelihood for each observation of the model evaluated at params. See Notes
- loglike
Notes
\[\ln L=\sum_{i=1}^{n}\left[\mu_{i}+(y_{i}-1)*ln(\mu_{i}+ \alpha*\mu_{i}^{p-1}*y_{i})-y_{i}*ln(1+\alpha*\mu_{i}^{p-1})- ln(y_{i}!)-\frac{\mu_{i}+\alpha*\mu_{i}^{p-1}*y_{i}}{1+\alpha* \mu_{i}^{p-1}}\right]\]for observations \(i=1,...,n\)