Inference for Bivariate Conway-Maxwell-Poisson Distribution and Its Application in Modeling Bivariate Count Data

Abstract

In recent actuarial literature, the bivariate Poisson regression model has been found to be useful for modeling paired count data. However, the basic assumption of marginal equi-dispersion may be quite restrictive in practice. To overcome this limitation, we consider here the recently developed bivariate Conway–Maxwell–Poisson (CMP) distribution. As a distribution that allows data dispersion, the bivariate CMP distribution is a flexible distribution which includes the bivariate Poisson, bivariate Bernoulli and bivariate Geometric distributions all as special cases. We discuss inferential methods for this CMP distribution. An application to automobile insurance data demonstrates its usefulness as an alternative framework to the commonly used bivariate Poisson model.