Rates of convergence of extremes from skew normal samples
  For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an optimal choice of norming constants. We find that the optimal convergence rate of the normalized maximum to the Gumbel extreme value distribution is proportional to $1/\log n$. 
Xin Liao, Zuoxiang Peng, Saralees Nadarajah, Xiaoqian Wang
stat.ME