statsmodels.discrete.discrete_model.GeneralizedPoisson.loglike

GeneralizedPoisson.loglike(params)

Loglikelihood of Generalized Poisson model

Parameters:params (array-like) – The parameters of the model. Returns:loglike – The log-likelihood function of the model evaluated at params. See notes. Return type:float

Notes

$$\ln L=\sum_{i=1}^{n}\left[\mu_{i}+(y_{i}-1)*ln(\mu_{i}+ \alpha*\mu_{i}^{p-1}*y_{i})-y_{i}*ln(1+\alpha*\mu_{i}^{p-1})- ln(y_{i}!)-\frac{\mu_{i}+\alpha*\mu_{i}^{p-1}*y_{i}}{1+\alpha* \mu_{i}^{p-1}}\right]$$