Convergence Rate of Extreme of Skew Normal Distribution Under Power Normalization

Authors: Huang Jianwen, Yang Hongyan

Let $\{X_n,~n\geq1\}$ be independent and identically distributed random variables with each $X_n$ following skew normal distribution. Let $M_n=\max\{X_k,~1\leq k\leq n\}$ denote the partial maximum of $\{X_n,~n\geq1\}$. 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.

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[v1] 2014-10-13 10:09:31

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