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On the asymptotically uniform distribution modulo 1 of extreme order statistics
Author(s) -
Wilms R. J. G.,
Brands J. J. A. M.
Publication year - 1994
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.1994.tb01431.x
Subject(s) - independent and identically distributed random variables , mathematics , modulo , order statistic , random variable , sequence (biology) , distribution (mathematics) , order (exchange) , combinatorics , statistics , uniform distribution (continuous) , mathematical analysis , finance , biology , economics , genetics
Let (X m )∞ 1 be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of rnax (X 1 ., X n ) to converge in distribution, as n ←∞ to a random variable with a uniform distribution on [0, 1).