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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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