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

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  • Gómez-Déniz, Emilio
  • Sarabia, José María
  • Balakrishnan, N.

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.

Suggested Citation

  • Gómez-Déniz, Emilio & Sarabia, José María & Balakrishnan, N., 2012. "A Multivariate Discrete Poisson-Lindley Distribution: Extensions and Actuarial Applications," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 655-678, November.
    • Handle: RePEc:cup:astinb:v:42:y:2012:i:02:p:655-678_00
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    Cited by:

    1. Muhammed Rasheed Irshad & Christophe Chesneau & Veena D’cruz & Naushad Mamode Khan & Radhakumari Maya, 2022. "Bivariate Poisson 2Sum-Lindley Distributions and the Associated BINAR(1) Processes," Mathematics, MDPI, vol. 10(20), pages 1-24, October.
    2. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    3. Juliana Schulz & Christian Genest & Mhamed Mesfioui, 2021. "A multivariate Poisson model based on comonotonic shocks," International Statistical Review, International Statistical Institute, vol. 89(2), pages 323-348, August.

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