Composite Lognormal-T regression models with varying threshold and its insurance application

Abstract

Composite probability models have shown very promising results for modeling claim severity data comprised of small, moderate, and large losses. In this paper, we introduce three classes of parametric composite regression models with a varying threshold. We consider the Lognormal distribution for the head and the Burr, the Stoppa and the generalized log-Moyal (GlogM) distributions for the tail part of the composite family. Further, the Mode-Matching procedure has been utilized for the composition of the two densities. To capture the heterogeneous behavior of the policyholder's characteristics, covariates are introduced into the scale parameter of the tail distribution. Finally, the applicability of the proposed models has been shown using a real-world insurance data set.