Tweedie类分布下广义线性联合均值与散度混合专家回归模型

Mixture of Expert Regression for Joint Mean and Dispersion Models Based on the Tweedie Distribution Family

Tweedie类分布在财产保险中常常用来对索赔额进行量化,而混合专家回归模型在统计和机器学习方面被广泛地研究,并用来对异质总体数据进行分类、聚类及回归分析.本文基于Tweedie类分布提出广义线性联合均值与散度混合专家回归模型,从而为非寿险费率厘定精算技术的发展提供参考思路.接着,利用EM算法给出该模型的极大似然估计,进而通过随机模拟实验验证了所提出方法的有效性.最后,本文结合空气质量指标(AQI)数据验证了该模型和方法具有实用性和可行性.

In property insurance, the Tweedie distribution family is widely used for analysis of claim.Mixture of expert regression models are widely studied in statistics and machine learning for modeling heterogeneity in data for regression, clustering and classification. We propose mixture of expert regression for joint mean and dispersion models based on the Tweedie distribution family to provide a reference for the development of actuarial technology for non-life insurance ratemaking. Then, EM algorithm is considered to estimate unknown parameters in the maximum likelihood estimation procedure. Furthermore, the parameter estimation performance of proposed model is evaluated through simulation studies. Finally,the results from the analysis of a real data set from air quality index data are presented to illustrate the proposed theory and methodology.