保险索赔次数的零点修正分布及其参数估计方法

Zero-Modified Distributions for Claim Numbers and Its Parameter Estimation

在保险精算中,对索赔次数分布的估计是费率厘定过程中的重要环节。索赔次数的分布通常在零点具有较大的概率,现有的标准分布无法较好地实现对零点概率的拟合,因此,需要对零点概率进行修正,从而生成零点修正分布。文章讨论了零点修正分布参数的极大似然估计、贝叶斯估计以及矩方法估计,并以零点修正的泊松分布和零点修正的几何分布为例,对一组实际索赔次数的样本数据进行了估计。结果表明零点修正分布的估计效果明显优于原始分布,在三种估计方法中,贝叶斯估计具有最好的拟合效果。

In actuarial science, the estimation of the distribution for claim numbers is an important part of ratemaking. The distribution of claim numbers has large probability at zero in general, while traditional standard distribution usually fails to have a good fit at zero. On this account, it is necessary to modify the probability at zero to generate zero-modified distributions. This pa- per discusses maximum likelihood estimation of zero-modified distribution parameters, Bayesian estimation and method of mo- ments, and also takes zero-modified Poisson and geometric distributions as examples to estimate a set of sample data of actual claim numbers. The study result shows that zero-modified distributions have better performance than original distributions, and that Bayesian estimation has the best fitting performance among the three estimation methods.