EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking

Abstract

This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the Poisson-Inverse Gamma regression model with varying dispersion. The empirical analysis examines a portfolio of motor insurance data in order to investigate the efficiency of the proposed algorithm. Finally, both the a priori and a posteriori, or Bonus-Malus, premium rates that are determined by the Poisson-Inverse Gamma model are compared to those that result from the classic Negative Binomial Type I and the Poisson-Inverse Gaussian distributions with regression structures for their mean and dispersion parameters.