A bivariate extension of three-parameter generalized crack distribution for loss severity modelling

Abstract

In this paper, we introduce a bivariate extension of three-parameter generalized crack distribution for modelling loss data. Some basic properties such as the conditional distribution and the measures of association are discussed, and a method of parameter estimation is offered. A simulation-based approach to compute bivariate value-at-risk under the model is also discussed. The proposed model and estimation method are illustrated with a model fitting exercise on a real catastrophic loss data set.