幂指数泊松分布的再认识
The exponentiated exponential Poisson distribution revisited
摘要：
通过给出三参数指数Poisson概率分布${\rm EEP}(α, β, λ)$的特征函数$ϕ_ξ(t)$和矩母函数$M_ξ(t)$的显式封闭形式表达式，刻画和研究了三参数指数Poisson概率分布${\rm EEP}(α, β, λ)$，并证明了已有的正整数阶矩$\mathbb Eξ^ν, ν\in \mathbb N$的级数和积分形式表达式对所有$ν>1-α, α>0$都是有效的.
英文摘要：
The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution ${\rm EEP}(α, β, λ)$ by giving explicit closed form expressions for its characteristic function $ϕ_ξ(t)$ and moment generating function $M_ξ(t)$, and finally, to show that the existing series and integral form expressions for positive integer order moments $\mathbb Eξ^ν, ν\in \mathbb N$ are in fact valid for all $ν>1-α, α>0$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
