## 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 $$[0,1)$$.

### MSC:

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

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