  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.
