A new class of composite GBII regression models with varying threshold for modelling heavy-tailed data

TL;DR

This paper introduces a novel composite GBII regression model with a varying threshold to effectively model heavy-tailed insurance loss data, capturing heterogeneity and small-large claim dynamics.

Contribution

It proposes a new composite GBII regression approach with a variable threshold, incorporating covariates for improved modeling of heavy-tailed insurance losses.

Findings

Simulation confirms estimation accuracy and model flexibility.

Application to real datasets demonstrates superior fit compared to existing models.

The model effectively captures heterogeneity and tail behavior in insurance data.

Abstract

The four-parameter generalized beta distribution of the second kind (GBII) has been proposed for modelling insurance losses with heavy-tailed features. The aim of this paper is to present a parametric composite GBII regression modelling by splicing two GBII distributions using mode matching method. It is designed for simultaneous modeling of small and large claims and capturing the policyholder heterogeneity by introducing the covariates into the location parameter. In such cases, the threshold that splits two GBII distributions varies across individuals policyholders based on their risk features. The proposed regression modelling also contains a wide range of insurance loss distributions as the head and the tail respectively and provides the close-formed expressions for parameter estimation and model prediction. A simulation study is conducted to show the accuracy of the proposed estimation method and the flexibility of the regressions. Some illustrations of the applicability of the new class of distributions and regressions are provided with a Danish fire losses data set and a Chinese medical insurance claims data set, comparing with the results of competing models from the literature.