零膨胀广义泊松模型的推广及其在精算中应用  

Generalization of Zero-inflated Generalized Poisson Model and Its Application in Actuarial Science

作　　者：徐昕[1] XU Xin(School of Finance,Capital University of Economics and Business,Beijing 100070,China)

机构地区：[1]首都经济贸易大学金融学院,北京100070

出　　处：《数理统计与管理》2020年第6期1010-1021,共12页Journal of Applied Statistics and Management

基　　金：国家自然科学基金项目(71701138);2017年中国保监会部级课题项目。

摘　　要：精算中在建立索赔次数预测模型时往往会遇到零膨胀(zero-inflated)问题,多数情况不能用传统的泊松模型拟合。过多的零次索赔又会导致过离散即方差大于均值(over dispersion)问题,从而低估参数的标准误差,高估显著性水平。本文重点对两类零膨胀广义泊松模型ZIGP-1和ZIGP-2推广,将其拓展为更一般的ZIGP-P形式(P为参数),嵌套了ZIGP-1和ZIGP-2模型。当P=1和P=2时,ZIGP-P模型即退化为ZIGP-1和ZIGP-2模型。最后,利用推广的ZIGP-P模型对一组保险索赔数据拟合,结果表明,ZIGP-P模型在处理零膨胀问题时可以有效地改善拟合效果。Claim counts data in insurance are often zero-inflated,and traditional Poisson model may not fit well usually.Extra zeros in claim counts may result in an over-dispersion problem,which underestimates the standard errors of parameters and overestimates the significance level.This paper extends two types of generalized Poisson models ZIGP-1 and ZIGP-2 to a more general form model ZIGP-P.When p=1 and p=2,the ZIGP-P model degrades to ZIGP-1 and ZIGP-2 models.Finally,the ZIGP-P model is used to fits a set of insurance claim data.The results show ZIGP-P model can improve the good ness-of-fit effectively when dealing with zero-inflated data.

关 键 词：零膨胀 广义泊松 推广 应用 

分 类 号：O212[理学—概率论与数理统计]