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An Elementary Proof of the Order-Statistics Characterization of the Poisson Process

 

作者: Gaoxiong Gan,   Shie-Shien Yang,  

 

期刊: The American Statistician  （Taylor Available online 1989）
卷期: Volume 43, issue 1  

页码: 45-46

 

ISSN:0003-1305

 

年代: 1989

 

DOI:10.1080/00031305.1989.10475609

 

出版商: Taylor & Francis Group

 

关键词: Arrival times;Interarrival times;Nonhomogeneous Poisson process;Renewal process

 

数据来源: Taylor

 

摘要:

A continuous-time renewal process (N(t),t≥ 0) is a Poisson process if and only if the conditional distribution of an interarrival time givenN(t) =nis the same as that of the minimum order statistic corresponding tonindependent random variables identically and uniformly distributed on the interval [0,t). Similar characterization is also given for a nonhomogeneous Poisson process.

 

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