A Multivariate Discrete Poisson-Lindley Distribution Extensions and Actuarial Applications

This paper proposes multivariate versions of the continuous Lindley mixture of Poisson distributions considered by Sankaran (1970). This new class of distributions can be used for modelling multivariate dependent count data when marginal overdispersion is present. After discussing some of its properties, a general multivariate model with Poisson-Lindley marginals and with a flexible covariance structure is proposed. Several specific models as well as one that allows correlations of any sign are considered, and then some estimation methods are discussed. Finally, some illustrative examples are given for fitting and demonstrating the usefulness of these bivariate distributions.

Keywords: Actuarial, Bonus-Malus, Frequency Distribution, Poisson-Lindley Distribution, Regression, Sarmanov-Lee Family