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On characterizations of the geometric distribution by independence of functions of order statistics

Published online by Cambridge University Press:  14 July 2016

R. C. Srivastava
R. C. Srivastava*
Affiliation:
The Ohio State University
*
∗Postal address: Department of Statistics The Ohio State University, 113 Cockins Hall, 1958 Neil Avenue, Columbus, OH 43210–1247, USA.
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Abstract

Let X1, · ··, Xn, n ≧ 2 be i.i.d. random variables having a geometric distribution, and let Y1 ≦ Y2 ≦ · ·· ≦ Yn denote the corresponding order statistics. Define Rn = Yn – Y1 and Zn = Σj=2n (Υj – Y1). Then it is well known that (i) Y, and Rn are independent and (ii) Y1 and Zn are independent. In this paper, we show that a very weak form of each of these independence properties is a characterizing property of the geometric distribution in the class of discrete distributions.

Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 227 - 232
Copyright
Copyright © Applied Probability Trust 1986 

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