On the asymptotically uniform distribution modulo 1 of extreme order statistics. (English) Zbl 0826.62013

Summary: Let \((X_m )^\infty_1\) be a sequence of independent and identically distributed random variables. We give sufficient conditions for the fractional part of \(\max (X_1, \dots, X_n)\) to converge in distribution, as \(n\to \infty\), to a random variable with a uniform distribution on \([0,1)\).


62E20 Asymptotic distribution theory in statistics
62G30 Order statistics; empirical distribution functions
60F05 Central limit and other weak theorems
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