Asymptotically Uniform Distribution Modulo 1 of Extreme Order Statistics (Revised Version)

摘要

Let (X(sub m)) from 1 to infinity be a sequence of independent and identically distributed random variables. The authors give sufficient conditions for the fractional part of max (X(sub 1),...,X(sub n)) to converge in distribution, as n -> infinity to a random variable with a uniform distribution on the interval 0,1, closed to the left, open to the right.