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May, 1977 A Characteristic Property of the Exponential Distribution
M. Ahsanullah
Ann. Statist. 5(3): 580-582 (May, 1977). DOI: 10.1214/aos/1176343860

Abstract

Let $X$ be a nonnegative random variable with probability distribution function $F$. Suppose $X_{i,n} (i = 1,\cdots, n)$ is the $i$th smallest order statistics in a random sample of size $n$ from $F$. A necessary and sufficient condition for $F$ to be exponential is given which involves the identical distribution of the random variables $X$ and $(n - i) (X_{i+1,n} - X_{i,n})$ for some $i$ and $n$, $(1 \leqq i < n)$.

Citation

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M. Ahsanullah. "A Characteristic Property of the Exponential Distribution." Ann. Statist. 5 (3) 580 - 582, May, 1977. https://doi.org/10.1214/aos/1176343860

Information

Published: May, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0381.62012
MathSciNet: MR438547
Digital Object Identifier: 10.1214/aos/1176343860

Subjects:
Primary: 62E10
Secondary: 62G30

Keywords: characterization , exponential distribution , identical distribution , order statistics

Rights: Copyright © 1977 Institute of Mathematical Statistics

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Vol.5 • No. 3 • May, 1977
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