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December 1997 Generalized zero-one laws for large-order statistics
Hong Wang
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Bernoulli 3(4): 429-444 (December 1997).


For a fixed integer r 1 , let Z rn be the r th largest of { X 1,X 2,...,X n} , where X 1 ,X 2,... is a sequence of i.i.d. random variables with the common distribution fuction F (x) . We prove that P {Z rn u n, i.o.}= 0 or 1 accordingly as the series n =1 exp[-n{1-F(u n)}][n{1-F(u n)}] r/n< or = for any real sequence { u n} such that lim n n{1-F(u n)}=+ . This weakens the condition added on the sequence [ n{1-F(u n)}] by Wang and Tomkins and generalizes the results of Klass to the case when r 1 .


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Hong Wang. "Generalized zero-one laws for large-order statistics." Bernoulli 3 (4) 429 - 444, December 1997.


Published: December 1997
First available in Project Euclid: 6 April 2007

zbMATH: 0910.60020
MathSciNet: MR1483697

Keywords: i.i.d. random variables , large-order statistics , Zero-one law

Rights: Copyright © 1997 Bernoulli Society for Mathematical Statistics and Probability

Vol.3 • No. 4 • December 1997
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