# On the asymptotically uniform distribution modulo 1 of extreme order statistics

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

## 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 language English Eindhoven Technische Universiteit Eindhoven 12 Revised Published - 1992

### Publication series

Name Memorandum COSOR 9138 0926-4493

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