The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk

Abstract

The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and skewed to the right. Therefore, these distributions are well suited to fit count data with these properties. Furthermore, recent studies in actuarial sciences argue for the consideration of such distributions in the computation of risk factors. In this paper, we provide a thorough analysis of the LAEDM by deriving (a) the mean value parameterization of the LAEDM; (b) exact expressions for its probability mass function at n=0,1,…; (c) a simple bound for these probabilities that is sharp for large n; (d) a simulation algorithm for sampling from LAEDM. We have implemented the LAEDM for statistical modeling of various real count data sets. We assess its fitting performance by comparing it with the performances of traditional counting models. We use a simulation algorithm for computing tail probabilities of the aggregated claim size in an insurance risk model.

Keywords

• natural exponential family
• exponential dispersion model
• variance function
• count data
• Monte Carlo simulation