A Regression Model Based on Double Parameters Poisson Distribution and Its Applications to Risk Classification

A distribution about claim numbers has been introduced and the regression based on the distribution has been investigated in this paper. This distribution including double parameters, which is over-dispersion about Poisson, can be applied on risk classification. Statistics inference can be used to analyze the departure from Poisson model by testing the parameter of over-dispersion. Two classical examples on risk classification are studied again, one is about ship damage numbers and another is about car claims.