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A Bivariate Extension of Type-II Generalized Crack Distribution for Modeling Heavy-Tailed Losses

Author

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  • Taehan Bae

    (Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada
    These authors contributed equally to this work.)

  • Hanson Quarshie

    (University of Regina, Regina, SK S4S 0A2, Canada
    These authors contributed equally to this work.)

Abstract

As an extension of the (univariate) Birnbaum–Saunders distribution, the Type-II generalized crack (GCR2) distribution, built on an appropriate base density, provides a sufficient level of flexibility to fit various distributional shapes, including heavy-tailed ones. In this paper, we develop a bivariate extension of the Type-II generalized crack distribution and study its dependency structure. For practical applications, three specific distributions, GCR2-Generalized Gaussian, GCR2-Student’s t , and GCR2-Logistic, are considered for marginals. The expectation-maximization algorithm is implemented to estimate the parameters in the bivariate GCR2 models. The model fitting results on a catastrophic loss dataset show that the bivariate GCR2 distribution based on the generalized Gaussian density fits the data significantly better than other alternative models, such as the bivariate lognormal distribution and some Archimedean copula models with lognormal or Pareto marginals.

Suggested Citation

  • Taehan Bae & Hanson Quarshie, 2024. "A Bivariate Extension of Type-II Generalized Crack Distribution for Modeling Heavy-Tailed Losses," Mathematics, MDPI, vol. 12(23), pages 1-26, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3718-:d:1530510
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    References listed on IDEAS

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