复合离散型随机变量分布的迭代计算公式

An evaluation for a compound discrete distribution

在各种风险模型中,一般以复合随机变量来刻画索赔过程或收入过程,文中讨论了一类复合离散随机变量的概率分布问题,在个体索赔服从离散型分布的情形下,证明了概率分布的迭代计算公式,最后给出一个数值例子.

In various risk models, the claim process or income process is usually described by compound random variables.In this paper a recursive formula of distribution of total claims is develop for a family, when the number the claim amount is discrete the recursive formula can be used to compute the distribution of total claims.For illustration purposes, we give a numerical example in the end of the paper.