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

TL;DR

This paper introduces new composite regression models with varying thresholds, combining Lognormal and other distributions for insurance claim severity, and demonstrates their effectiveness on real data.

Contribution

It proposes three novel composite regression models with varying thresholds, incorporating covariates into the tail distribution for improved insurance claim modeling.

Findings

Models effectively capture claim severity heterogeneity.

Application to real insurance data shows good fit.

Enhanced modeling of small, moderate, and large losses.

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.