On the Composite Weibull–Burr Model to describe claim data

Abstract

ABSTRACTIn this article, a new continuous composite model, useful for modeling losses that combine a mixture of moderate and large claims, is presented. The probability density function of this family, the composite Weibull–Burr distribution, is unimodal and positively skewed with a thick upper tail. This model is derived, via a mode-matching procedure, by using the Weibull distribution up to the modal value (threshold) and the scaled Burr density thereafter. This methodology ensures not only the continuity and differentiability conditions at the threshold, but it also facilitates its computational implementation. The performance of this composite model is compared with the Weibull–Burr spliced distribution, continuous composite Weibull–Pareto and Weibull–Pareto spliced families, and the GB2 distribution in the context of the well-known Danish fire insurance dataset.