On the asymptotically uniform distribution modulo 1 of extreme order statistics

J.J.A.M. Brands, R.J.G. Wilms

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Abstract

Let $(X-m)^\infty_1$ be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of $max(X_1, ..., X_n)$ to converge in distribution, as $n \rightarrow \infty$, to a random variable with a uniform distribution on [0,1). Key Words & Phrases: distribution (modulo 1), Fourier-Stieltjes coefficients, fractional part.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages12
EditionRevised
Publication statusPublished - 1992

Publication series

NameMemorandum COSOR
Volume9138
ISSN (Print)0926-4493

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