Asymptotic expansions of powered skew-normal extremes

Let M-n denote the partial maximum of a sequence of independent random variables with common skew-normal distribution F-lambda(x) with parameter lambda. 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 vertical bar M-n vertical bar(t) to its ultimate extreme value distribution is the order of 1/(log n)(2) as t = 2, and the convergence rate is the order of 1/log n for the case of 0 < t not equal 2.