Asymptotic expansions of powered skew-normal extremes

Abstract

Let Mn denote the partial maximum of a sequence of independent random variables with common skew-normal distribution Fλ(x) with parameter λ. In this paper, higher-order distributional expansions and convergence rates of powered skew-normal extremes are considered. It is shown that with optimal normalizing constants the convergence rate of the distribution of |Mn|t to its ultimate extreme value distribution is the order of 1∕(logn)2 as t=2, and the convergence rate is the order of 1∕logn for the case of 0<t≠2.