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A multivariate Poisson model based on comonotonic shocks

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  • Juliana Schulz
  • Christian Genest
  • Mhamed Mesfioui

Abstract

Multivariate count data arise naturally in practice. In analysing such data, it is critical to define a model that can accurately capture the underlying dependence structure between the counts. To this end, this paper develops a multivariate model wherein correlated Poisson margins are generated by a comonotonic shock vector. The proposed model allows for greater flexibility in the dependence structure than that of the classical construction, which relies on the convolution of vectors of common Poisson shock variables. Several probabilistic properties of the multivariate comonotonic shock Poisson model are established, and various estimation strategies are discussed in detail. The model is further studied through simulations, and its utility is highlighted using a real data application.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:2:p:323-348
    DOI: 10.1111/insr.12408
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    References listed on IDEAS

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    1. Sellers, Kimberly F. & Morris, Darcy Steeg & Balakrishnan, Narayanaswamy, 2016. "Bivariate Conway–Maxwell–Poisson distribution: Formulation, properties, and inference," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 152-168.
    2. Dimitris Karlis, 2003. "An EM algorithm for multivariate Poisson distribution and related models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 63-77.
    3. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    4. Anastasios Panagiotelis & Claudia Czado & Harry Joe, 2012. "Pair Copula Constructions for Multivariate Discrete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1063-1072, September.
    5. Michael S. Smith & Mohamad A. Khaled, 2012. "Estimation of Copula Models With Discrete Margins via Bayesian Data Augmentation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 290-303, March.
    6. Genest, Christian & Mesfioui, Mhamed & Schulz, Juliana, 2018. "A new bivariate Poisson common shock model covering all possible degrees of dependence," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 202-209.
    7. van Ophem, Hans, 1999. "A General Method To Estimate Correlated Discrete Random Variables," Econometric Theory, Cambridge University Press, vol. 15(2), pages 228-237, April.
    8. Pfeifer, Dietmar & Nešlehová, Johana, 2004. "Modeling and Generating Dependent Risk Processes for IRM and DFA," ASTIN Bulletin, Cambridge University Press, vol. 34(2), pages 333-360, November.
    9. 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.
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