负二项回归模型的推广及其在分类费率厘定中的应用

Generalization of Negative Binomial Regression Model and Its Application to Classification Ratemaking

分类费率厘定中最常使用的模型之一是泊松回归模型,但当损失次数数据存在过离散特征时,通常会采用负二项回归模型。本文将两参数的负二项回归模型推广到了三参数情况,并用它来解决分类费率厘定中的过离散(over-dispersion)问题。本文通过对一组汽车保险损失数据的拟合表明,三参数的负二项分布回归模型可以有效改善对实际损失数据的拟合效果。

Poisson regression model is widely used in classification ratemaking,and when the data appear to be over-dispersed,negative binomial regression model will be applied.In order to deal with over-dispersion in the data,the paper extends the negative binomial distribution and makes it have three parameters.At the end of the paper,we apply the extended model to a loss data set of automobile insurance and the result shows that the goodness-of-fit can be effectively improved.