k阶几何无穷可分分布族(英文)

The Class of Sum-Geometric Infinitely Divisible Distributions of Order k

一个非退化的m维随机向量Y称为是k阶几何无穷可分的，是指对任何0＜p＜1，存在独立同分布的m维随机向量{Ypi,i≥1}使得Y=,其中Np为取正整数随机变量，服从参数为p和k的广义几何分布，且Np与{Ypi,i≥1）独立．本文给出了这类分布的刻划和应用．

A non-degenerate m-dimensional random vector Y is called sum-geometric infinitely di visible of order k if for cach 0<p<1 therc exist m-dimensional independent and identically distributed random vectors {Ypi,i≥1),independent of a positive integer random variable Np^Geometric(p,k),the extended geometric distribution with parameters p and k, such that Y= These distributions are characterized, and examples and applications are given.