最大最小顺序统计量的相关结构

摘要

Assume (X1,Y1),(X2,Y2),…,(Xn,Yn) are simple random samples from the two dimensiona population (X,Y) which has a distribution function H(x,y),let(X(1)=min1≤1≤n{Xi}),(X(n)=max1≤1≤n{Xi}),(Y(1)=min1≤1≤n{Yi}),(Y(n)=max1≤1≤n{Yi}) . The dependence structure about (X(1),Y(n)),(X(1),Y(1)) and (X (n),Y(n)) ar studied through Copula, and some examples are given to illustrate its applications. The fact shows that the dependence structure between maximum and minimum order statistic contain common product Copula, FGM and so on, which provide a new idea for constructing copula.%(X1,Y1),(X2,Y2),…,(Xn,Yn)为来自二维总体(X,Y)的简单随机样本,(X,Y)具有分布函数H(x,y),(X(1)=min1≤1≤n{Xi}),(X(n)=max1≤1≤n{Xi}),(Y(1)=min1≤1≤n{Yi}),(Y(n)=max1≤1≤n{Yi}).利用Copula研究了(X(1),Y(n))、(X(1),Y(1))及(X(n),Y(n))的相关结构,并举例说明了其应用.事实表明,最大最小顺序统计量的相关结构包括常见的积Copula和FGM等,为构造Copula提供了新思路.