标题： 指数指数泊松分布再访 显示英文标题

标题： The exponentiated exponential Poisson distribution revisited

摘要： 本文的主要目的是刻画并研究三参数指数广义泊松概率分布${\rm EEP}(\alpha, \beta, \lambda)$，通过给出其特征函数$\phi_\xi(t)$和矩生成函数$M_\xi(t)$的明确封闭形式表达式，最后证明正整数阶矩的现有级数和积分形式表达式$\mathbb E\xi^\nu, \nu \in \mathbb N$实际上对所有$\nu>1-\alpha, \alpha>0$都成立。 显示英文摘要

摘要： The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution ${\rm EEP}(\alpha, \beta, \lambda)$ by giving explicit closed form expressions for its characteristic function $\phi_\xi(t)$ and moment generating function $M_\xi(t)$, and finally, to show that the existing series and integral form expressions for positive integer order moments $\mathbb E\xi^\nu, \nu \in \mathbb N$ are in fact valid for all $\nu>1-\alpha, \alpha>0$.