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Bivariate mixed Poisson regression models with varying dispersion

Tzougas, George and di Cerchiara, Alice Pignatelli (2021) Bivariate mixed Poisson regression models with varying dispersion. North American Actuarial Journal. ISSN 1092-0277

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Identification Number: 10.1080/10920277.2021.1978850


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

Item Type: Article
Official URL:
Additional Information: © 2021 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 11 Mar 2022 14:33
Last Modified: 17 Mar 2022 09:00

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