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A bivariate count model with discrete Weibull margins

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  • Barbiero, A.

Abstract

Multivariate discrete data arise in many fields (statistical quality control, epidemiology, failure and reliability analysis, etc.) and modelling such data is a relevant task. Here we consider the construction of a bivariate model with discrete Weibull margins, based on Farlie–Gumbel–Morgenstern copula, analyse its properties especially in terms of attainable correlation, and propose several methods for the point estimation of its parameters. Two of them are the standard one-step and two-step maximum likelihood procedures; the other two are based on an approximate method of moments and on the method of proportion, which represent intuitive alternatives for estimating the dependence parameter. A Monte Carlo simulation study is presented, comprising more than one hundred artificial settings, which empirically assesses the performance of the different estimation techniques in terms of statistical properties and computational cost. For illustrative purposes, the model and related inferential procedures are fitted and applied to two datasets taken from the literature, concerning failure data, presenting either positive or negative correlation between the two observed variables. The applications show that the proposed bivariate discrete Weibull distribution can model correlated counts even better than existing and well-established joint distributions.

Suggested Citation

  • Barbiero, A., 2019. "A bivariate count model with discrete Weibull margins," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 91-109.
    • Handle: RePEc:eee:matcom:v:156:y:2019:i:c:p:91-109
    DOI: 10.1016/j.matcom.2018.07.003
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    References listed on IDEAS

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    1. Cambanis, Stamatis, 1977. "Some properties and generalizations of multivariate Eyraud-Gumbel-Morgenstern distributions," Journal of Multivariate Analysis, Elsevier, vol. 7(4), pages 551-559, December.
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    6. James D. Englehardt & Ruochen Li, 2011. "The Discrete Weibull Distribution: An Alternative for Correlated Counts with Confirmation for Microbial Counts in Water," Risk Analysis, John Wiley & Sons, vol. 31(3), pages 370-381, March.
    7. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
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    Cited by:

    1. Abdulhamid A. Alzaid & Weaam M. Alhadlaq, 2023. "A New Family of Archimedean Copulas: The Half-Logistic Family of Copulas," Mathematics, MDPI, vol. 12(1), pages 1-18, December.

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