A new poisson mixture model for the number of claims in automobile insurance

Abstract

Modelling the claim frequency is one of the most important issues in Risk Theory. In this chapter, two new probability distribution are introduced, a two-parameter probability density function, including a wide variety of curve shapes, and a two-parameter probability mass function. The latter, obtained by mixing the classical Poisson distribution with the former, will be applied to fit a large collection of data set concerning automobile insurance claims. The probability mass function of this new distribution has a closed form and presents excellent properties. The suitability of the new model proposed is illustrated in setting third party liability automobile insurance compared with alternative models traditionally used in the literature.