Asymptotic expansions of powered skew-normal extremes

Abstract Let M n denote the partial maximum of a sequence of independent random variables with common skew-normal distribution F λ ( 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 | M n | 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 ≠ 2 .