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

Taehan Bae () and Hanson Quarshie
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Taehan Bae: Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada
Hanson Quarshie: University of Regina, Regina, SK S4S 0A2, Canada

Mathematics, 2024, vol. 12, issue 23, 1-26

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.

Keywords: heavy-tailed distribution; type-II generalized crack distribution; Spearman’s rho; Kendall’s tau; EM algorithm; catastrophic loss (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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