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Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution

Author

Listed:
  • Catalina Bolancé

    (RISKCENTER, Universitat de Barcelona)

  • Raluca Vernic

    (Faculty of Mathematics and Informatics, Ovidius University of Constanta)

Abstract

Starting from the question: “What is the accident risk of an insured?”, this paper considers a multivariate approach by taking into account three types of accident risks and the possible dependence between them. Driven by a real data set, we propose three trivariate Sarmanov distributions with generalized linear models (GLMs) for marginals and incorporate various individual characteristics of the policyholders by means of explanatory variables. Since the data set was collected over a longer time period (10 years), we also added each individual’s exposure to risk. To estimate the parameters of the three Sarmanov distributions, we analyze a pseudo-maximumlikelihood method. Finally, the three models are compared numerically with the simpler trivariate Negative Binomial GLM.

Suggested Citation

  • Catalina Bolancé & Raluca Vernic, 2017. "Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution," Working Papers XREAP2017-07, Xarxa de Referència en Economia Aplicada (XREAP), revised Nov 2017.
    • Handle: RePEc:xrp:wpaper:xreap2017-07
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    File URL: http://www.xreap.cat/RePEc/xrp/pdf/XREAP2017-07.pdf
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    Cited by:

    1. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.

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