On the asymptotic behavior of the expectation of the maximum of i.i.d. random variables

Abstract

We study the asymptotic behavior of the expectation of the maximum of n i.i.d. random variables drawn from a fixed distribution F, with finite expectation. In this setting, Downey (1990) [4] showed that this expectation grows as o(n). We provide an alternative simpler proof of Downey's result together with a tight lower bound.