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A Multivariate Discrete Poisson-Lindley Distribution: Extensions and Actuarial Applications

Published online by Cambridge University Press:  09 August 2013

Emilio Gómez-Déniz ,
José María Sarabia  and
N. Balakrishnan
José María Sarabia
Affiliation:
Department of Economics, University of Cantabria, Santander, Spain
N. Balakrishnan
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, CanadaL8S 4K1
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Abstract

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

ActuarialBonus-MalusFrequency DistributionPoisson-Lindley DistributionRegressionSarmanov-Lee Family
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 2 , November 2012 , pp. 655 - 678
Copyright
Copyright © International Actuarial Association 2012

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