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

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

Stat. Neerl. 48, No. 1, 63-70 (1994).

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 \([0,1)\).

MSC:

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

Keywords:

extreme order statistics; distribution (modulo 1); Fourier-Stieltjes coefficients; sufficient conditions; fractional part; uniform distribution

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