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

The four-parameter generalized beta distribution of the second kind (GBII) has been proposed for modeling insurance losses with heavy-tailed features. The aim of this paper is to present a parametric composite GBII regression modeling 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 scale parameter. The threshold that splits two GBII distributions is allowed to vary across individuals policyholders based on their risk features. The proposed regression modeling 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.