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A characterization of the geometric distribution
Published online by Cambridge University Press: 14 July 2016
Abstract
Let X1, X2, …, Xn be independent identically distributed positive integer-valued random variables with order statistics X1:n, X2:n, …, Xn:n. We prove that if the random variable X2:n – X1:n is independent of the events [X1:n = m] and [X1:n = k], for fixed k > m > 1, then the Xi's are geometric. This is related to a characterization problem raised by Arnold (1980).
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- Copyright © Applied Probability Trust 1983
Footnotes
Research carried out while the author was at Southern Illinois University at Carbondale.
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