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Two characterizations of the geometric distribution

Published online by Cambridge University Press:  14 July 2016

Barry C. Arnold
Barry C. Arnold*
Affiliation:
Iowa State University
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Abstract

Let X1, X2, …, Xn be independent identically distributed positive integer-valued random variables with order statistics X1:n, X2:n, …, Xn:n. If the Xi's have a geometric distribution then the conditional distribution of Xk+1:n – Xk:n given Xk+1:n – Xk:n > 0 is the same as the distribution of X1:n–k. Also the random variable X2:n – X1:n is independent of the event [X1:n = 1]. Under mild conditions each of these two properties characterizes the geometric distribution.

Keywords

CHARACTERIZATIONGEOMETRIC DISTRIBUTIONORDER STATISTICS
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 570 - 573
Copyright
Copyright © Applied Probability Trust 1980 

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References

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