On modeling claim frequency data in general insurance with extra zeros

In some occasions, claim frequency data in general insurance may not follow the traditional Poisson distribution and in particular they are zero-inflated. Extra dispersion appears as the number of observed zeros exceeding the number of expected zeros under the Poisson or even the negative binomial distribution assumptions. This paper presents several parametric zero-inflated count distributions, including the ZIP, ZINB, ZIGP and ZIDP, to accommodate the excess zeros for insurance claim count data. Different count distributions in the second component are considered to allow flexibility to control the distribution shape. The generalized Pearson χ2 statistic, Akaike's information criteria (AIC) and Bayesian information criteria (BIC) are used as goodness-of-fit and model selection measures. With the presence of extra zeros in a data set of automobile insurance claims, our result shows that the application of zero-inflated count data models and in particular the zero-inflated double Poisson regression model, provide a good fit to the data.