关于复合化n变量Poisson分布的构造及渐化式

THE RECURRENCE RELATIONS OF COMPOUNDED n-VARIATE POISSON DISTRIBUTION

三变量复合化Ｐｏｉｓｓｏｎ分布已由梁文骥讨论，所用的方法是把通常的三变量Ｐｏｉｓｓｏｎ分布Ｐ（τλ）与随机化参数τ进行复合．证明了许多分布，如Ｐｏｉｓｓｏｎ分布本身、负二项分布、Ｈｅｒｍｉｔｅ分布、ＮｅｙｍａｎＡ型分布以及Ｐｏｉｓｓｏｎ逆高斯分布，都可以从这个分布中得出．这种分布是Ｐｏｉｓｓｏｎ分布的一种一般化。本文把这种关系推广到了多变量情形．

The compounded Poisson distribution in trivariate has been discussed by Liang Wenji.The method of introduction is compounding usual trivariate Poisson distribution P(τλ) with a randomized parameter τ.The author claimed that many distributions such as Poisson distribution itself,negative binonial distribution,Hermite distribution,Neyman Type A distribution and Poisson Inverse-Gaussian distribution are derived from the distribution.The distribution is a kind of generalized Poisson.The purpose of this paper is to generalize these relations to multivariate case.