极值的极限分布的吸引场与二次极值之期望的极限律

THE DOMAINS OF ATTRACTION OF THE LIMIT DISTRIBUTIONS OF EXTREME AND THE LIMIT LAW OF THE EXPECTED VALUES OF DOUBLE EXTREME

设{Xi}im=1是i、i、d随机变量列,F（x）=P（Xi<x）。令Zm=mx（X1,X2,…,XM）,若存在实数列am及bm>0,对非退化的分布函数H（x）的一切连续点x,有 P（Zm<am+bmx）=H（x） （1）则称F（x）在H（x）的吸引场中,以F∈D（H）记之。由[1]可知H（x）只有三种类型。

Throughout this paper X_1, X_2, …, X_m denote i, i, d rondom variables with F(x)=P(X; <x). We put Z_m=max(X_1, X_2, …, X_m) and Y_m=(Z_m-a_m)/b_m, where am and b_m>0 are two sequence of real numbers. Y_m(n:n) denotes the Largest values from samples of size n of Y_m. The Y_m(n:n) are saied to be double maximumn. There, we have established relations betewn the domains of attraction of the. Limit distributions of extreme and Limt Laws of the expected values of double extreme