Convergence Rate of Extreme of Skew Normal Distribution under Power Normalization

Let {Xn, n ≥ 1} be independent and identically distributed random variables with each Xn following skew normal distribution. Let Mn = max{Xk, 1 ≤ k ≤ n} denote the partial maximum of {Xn, n ≥ 1}. Liao et al. (2014) considered the convergence rate of the distribution of the maxima for random variables obeying the skew normal distribution under linear normalization. In this paper, we obtain the asymptotic distribution of the maximum under power normalization and normalizing constants as well as the associated pointwise convergence rate under power normalization.