中文摘要：

设{Xk，1≤k≤n）独立同分布，x1,n,X2,n,…，xn：n为其顺序统计量．当xk服从三参数分别为u，σ，r（u∈R，σ〉0，r〉0）的Pareto分布时，作者得到了其极端顺序统计量X1,n和Xn：n的渐近分布；当k（k〉1）固定时，得到了Xk,n和Xn-k＋1,n的渐近分布，并且证明其极端顺序统计量X1：n和Xn：n是渐近独立的．

英文摘要：

Let {Xk ,1 ≤ k ≤ n} be independent and identically distributed random variables, and X1,n ,X2,n …, Xn：n be their order statistics. When Xk follows Pareto distribution with three parameters u,σ,r （u ∈ R,σ〉 0, r〉0）, the asymptotic distributions of their extreme order statistics X1,n and Xn,n are obtained. For a fixed integer k 〉 1, the asymptotic distributions of Xk,n and Xn-k＋1 are also obtained.What＇s more, it is proved that X1,n and Xn,n are asymptotically independent.