关于复合Poisson-Geometric分布的几个性质

Some properties of compound Poisson-Geometric distribution

在经典的风险模型中,描述赔付次数的过程是齐次Poisson过程.然而在保险实践中,风险事件与赔付事件有可能不是等价的,所以Poisson-Geometric分布比Poisson分布更为适合用来描述索赔次数的分布.利用随机变量的概率母函数研究复合Poisson-Geometric分布关于卷积的封闭性,并且讨论了复合Poisson-Geometric分布与复合Poisson分布以及复合广义负二项分布之间的关系.

In the classical risk models,the homogeneous Poisson process is used to describe the number of claims.However,the risk event and claim event are not equivalent in the practical insurance,Poisson-Geometric distribution is more appropriate for describing the claim numbers than Poisson distribution.Using the technique of probability generating function,we study the closure property of compound Poisson-Geometric distributions under convolution.We discuss the relationship between the compound Poisson-Geometric distribution and compound Poisson distribution.The relationship between compound generalized negative binomial distribution and compound Poisson-Geometric distribution is also investigated.