Bivariate Mixed Poisson Regression Models with Varying Dispersion

The main purpose of this article is to present a new class bivariate mixed Poisson regression models with varying dispersion that offers sufficient flexibility for accommodating overdispersion and accounting the positive correlation between number claims from third-party liability bodily injury property damage. Maximum likelihood estimation family achieved through an expectation-maximization algorithm shown have satisfactory performance when three members family, namely, negative binomial, Poisson–inverse Gaussian, Poisson–Lognormal distributions specifications on every parameter are fitted two-dimensional motor insurance data European insurer. posteriori, or bonus-malus, premium rates determined by these calculated via expected value variance principles compared those based only posteriori criteria. Finally, we extension proposed approach developing Normal copula-based model dependence parameters. This allows us consider influence individual coverage-specific risk factors mean, dispersion, copula parameters modeling different types coverage. For expository purposes, paired binomial marginals regressors simulated dataset maximum likelihood.