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

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, several specific distributions, GCR2-Generalized Gaussian, GCR2-Student’s t and GCR2-Logistic, are constructed. The expectation-maximization algorithm is implemented to estimate the parameters in the bivariate GCR2 models. The model fitting results on the catastrophic loss dataset show that the bivariate GCR2 distribution base on the generalized Gaussian density fits the data significantly better than other alternative models.