Two characterizations of the geometric distribution
1980 ◽
Vol 17
(02)
◽
pp. 570-573
◽
Keyword(s):
Let X 1, X 2, …, Xn be independent identically distributed positive integer-valued random variables with order statistics X 1:n , X 2: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 X 1:n–k . Also the random variable X 2:n – X 1:n is independent of the event [X 1:n = 1]. Under mild conditions each of these two properties characterizes the geometric distribution.
1983 ◽
Vol 20
(01)
◽
pp. 209-212
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2003 ◽
Vol 40
(01)
◽
pp. 226-241
◽
2003 ◽
Vol 40
(1)
◽
pp. 226-241
◽
2010 ◽
Vol DMTCS Proceedings vol. AN,...
(Proceedings)
◽
2021 ◽
Vol 73
(1)
◽
pp. 62-67
2012 ◽
Vol 49
(4)
◽
pp. 1188-1193
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Keyword(s):
1978 ◽
Vol 15
(03)
◽
pp. 639-644
◽