A characterization of the geometric distribution
1983 ◽
Vol 20
(01)
◽
pp. 209-212
◽
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 , …, X n:n . We prove that if the random variable X2:n – X 1: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).
1980 ◽
Vol 17
(02)
◽
pp. 570-573
◽
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