A Concise Proof of the Relation between Poisson Process and Exponential Distribution

作     者：TANG Ying\|hui,\ TANG Xiao\|wo Dept. of Appl. Math., Mgt.College, Univer. of Electronic Science and Technology of China, Chengdu 610054, China 

出 版 物：《Systems Science and Systems Engineering》 (系统科学与系统工程学报（英文版）)

年 卷 期：1999年第9卷第4期

页      面：40-43页

核心收录：

学科分类：0711[理学-系统科学] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 0811[工学-控制科学与工程] 081103[工学-系统工程] 

主　　题：exponential distribution memoryless property Poisson process 

摘      要：Using the memoryless property of the exponential distribution, we have proved again that the relation between the Poisson process and the exponential distribution, that is, the stochastic process {N(t), t≥0} is said to be a Poisson process with arrival rate λ(0) if and only if the sequence of interarrival times {τ n,n≥1} are independent and identically distributed according to an exponential distribution with parameter λ, where N(t) denotes the arrival number in (0,t\].. It′s noting that the proof provided in this paper is concise and intuitive.