Uniform convergence rates of skew-normal extremes

Let $M_n=\max \left(X_1, X_2, \ldots, X_n \right)$ 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 $1/\log n$.