Zero-inflated and over-dispersed data models: Empirical evidence from insurance claim frequencies

The main objective of this paper is to model automobile claim frequency by using standard count regression and zero-inflated regression models. The use of the latter model is mainly motivated by its ability to handle the over dispersion and zero-inflation phenomenon. The sample data consist of claims data obtained from one randomly selected automobile insurance company in Tunisia for a single year, 2009, containing beginning drivers and drivers who have had a license for less than three years. Our estimation results show that many exogenous variables can explain the frequency of claims; they are not taken into account in calculating the basic insurance premium. Moreover, the ZI binomial negative regression outperforms the standard count models and the ZI Poisson model in handling zero-inflated and additional over dispersed claim count data