A Suitable Discrete Distribution for Modelling Automobile Claim Frequencies

Abstract

A new discrete distribution, depending on two parameters, is introduced in this paper. A mixing process is utilized, with the discrete Lindley acting as the mixed and the Beta prime as the mixing distribution. The distribution obtained is shown to be unimodal and overdispersed. An equation for the probability density function of the compound version, when claim severities are exponentially distributed, is also derived. After reviewing some of its properties, we investigate the question of parameter estimation. Real frequency data consisting of automobile claim frequencies were fitted successfully using the proposed distribution and the estimated values were used to compute the right-tail probabilities of the aggregate claim size distribution when the new distribution acts as the primary distribution. These values are compared with those obtained when the Poisson distribution is assumed to be the primary distribution.