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.

翻译：针对具有重尾特征的保险损失数据，本文提出了一种四参数广义第二类贝塔分布（GBII）的复合回归模型。该模型通过模式匹配方法拼接两个GBII分布，旨在同时建模小额与大额索赔，并通过在位置参数中引入协变量来刻画投保人的异质性。在此框架下，分割两个GBII分布的阈值随个体投保人的风险特征动态变化。所提出的回归模型使头部与尾部能够分别涵盖广泛的保险损失分布，并提供参数估计与模型预测的闭合表达式。仿真研究表明，本文所提估计方法具有较高的精度，且回归模型具备良好的灵活性。通过丹麦火灾损失数据与中国医疗保险理赔数据的应用实例，本文验证了新分布与回归模型的实用性，并与文献中竞争模型的结果进行了对比分析。