Uniform convergence rates of skew-normal extremes

Let $M_n=\max (X_1,X_2,\dots ,X_n)$ 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 $(M_n-b_n)\mathrm{/}{a}_n$ to its ultimate extreme value distribution is proportional to $1\mathrm{/}\log n$.