Uniform convergence rates of skew-normal extremes

Abstract

Let $M_n=\max \left(X_1,X_2,\dots ,X_n\right)$ denote the partial maximum of an independent and identically distributed skew-normal random sequence. In this paper, the rate of uniform convergence of skew-normal extremes is derived. It is shown that with optimal normalizing constants the convergence rate of $\left(M_n-b_n\right)/a_n$ to its ultimate extreme value distribution is proportional to $1/\log n$.

19 pages