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

Authors
Gan, Gaoxiong Yang, Shie-Shien
Citation
Gan, Gaoxiong et Yang, Shie-shien, An Elementary Proof of the Order-Statistics Characterization of the Poisson Process, American statistician , 43(1), 1989, pp. 45-46
Journal title
American statistician → ACNP
ISSN journal
00031305
Volume
43
Issue
1
Year of publication
1989
Pages
45 - 46
Database
ACNP
SICI code
Abstract
A continuous-time renewal process (N(t), t . 0) is a Poisson process if and only if the conditional distribution of an interarrival time given N(t) = n is the same as that of the minimum order statistic corresponding to n independent random variables identically and uniformly distributed on the interval [0, t).Similar characterization is also given for a nonhomogeneous Poisson process.