statsmodels.discrete.discrete_model.GeneralizedPoisson.loglike¶

GeneralizedPoisson.loglike(params)[source]¶

Loglikelihood of Generalized Poisson model

Parameters:¶

paramsarray_like

The parameters of the model.

Returns:¶

loglikefloat

The log-likelihood function of the model evaluated at params. See notes.

Notes

$$\ln L=\sum _{i=1}^n[{\mu }_i+(y_i-1)\ast ln({\mu }_i+\alpha \ast {\mu }_i^{p-1}\ast y_i)-y_i\ast ln(1+\alpha \ast {\mu }_i^{p-1})-ln(y_i!)-\frac{{\mu }_i+\alpha \ast {\mu }_i^{p-1}\ast y_i}{1+\alpha \ast {\mu }_i^{p-1}}]$$