幂赋范下偏正态分布极值的收敛速度

On Convergence Rate of Extreme of Skew Normal Distribution under Power Normalization

令{Xn,n≥1}是独立同分布随机变量序列并且每个变量均服从偏正态分布.再令Mn=max{Xk,1≤k≤n}表示{Xn,n≥1}的部分最大值,得到了幂赋范下最大值分布的渐近分布和赋范常数以及幂赋范下相应的逐点收敛速度.

Let {X n ,n ≥ 1} be independent and identically distributed random variables with each following skew normal distribution .Let Mn = {X k ,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 ,the asymptotic distribution of the max‐imum has been obtained under power normalization and normalizing constants as well as the associated pointwise convergence rate under power normalization .