Buhlmann credibility model in predicting claim frequency that follows heterogeneous Weibull count distribution

Abstract

In insurance, policyholder’s claim experience is usually too limited to be given full credibility in predicting claim frequency, but policyholder’s risk is usually a part of a large risk class which collective claim experience can provide information for credible statistical prediction. Credibility could be used to consider both information. By assuming that the policyholder’s number of claims, given the policyholder’s risk parameter, follows Weibull count distribution over its risk class, this paper explains Buhlmann credibility in predicting claim frequency. Weibull count distribution relaxes the equidispersion assumption of Poisson distribution. Thus, Weibull count distribution can handle non-equidispersed count data. This paper also shows that for a certain type of past claim frequency data, the use of Poisson assumption in Buhlmann credibility model could result in very low credibility factor which underrates the policyholder’s experience.