摘要
给定n维分布F(x_1,…,x_n)与m维分布G(y_1,…,y_m),如果存在随机向量X=(X_1,…,X_n),Y=(Y_1,…,Y_m),使得X,Y分别以F, G为分布,X_i,Y_j(i=1,…,n;j=1,…,m)不相关并且不独立,则称F,G存在强耦合,且称n+m维随机向量(X_1,…,X_n,Y_1,…,Y_m)的分布就是F与G的一个强耦合。本文给出了F,G存在强耦合的一个充分条件和一个必要条件。特别地,当n≤2,m≤2时,文中所给的充分条件和必要条件恰好相重合。
Given n- and m-dimensional distribution functions F(X_1,…, X_n), G(Y_1,…,Y_n),we say that F and G have strong couplings if there exist two uncorrelated ran-dom vectors X=(X_1,…, X_n), Y=(Y_1,…,Y_n) and their distributions are F, Grespectively. In this case, the distribution of (X_1,…, X_n, Y_1,…, Y_m,) is called astrong coupling of F and G. In this paper, a necessary condition and a suffieientcondition for the existenee of strong couplings of F and G are given. In particular,for n≤2, m≤2, the both conditions are the same.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
1990年第3期1-6,共6页
Journal of East China Normal University(Natural Science)
关键词
多维分布函数
不相关
不独立
multivariate distribution
uncorrelation
independent weak distribution
strong distribation
