On characterizations of the geometric distribution by independence of functions of order statistics
Keyword(s):
Let X1, · ··, X n , n ≧ 2 be i.i.d. random variables having a geometric distribution, and let Y 1 ≦ Y 2 ≦ · ·· ≦ Y n denote the corresponding order statistics. Define Rn = Yn – Y 1 and Z n = Σ j=2 n (Υ j – Y1). Then it is well known that (i) Y, and Rn are independent and (ii) Y 1 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.
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1980 ◽
Vol 17
(02)
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pp. 570-573
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Keyword(s):
1983 ◽
Vol 20
(01)
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pp. 209-212
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2010 ◽
Vol 24
(2)
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pp. 245-262
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2007 ◽
Vol Vol. 9 no. 1
(Analysis of Algorithms)
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1987 ◽
Vol 24
(02)
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pp. 534-539
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2011 ◽
Vol 25
(4)
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pp. 435-448
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