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引用本文：	徐付霞,董永权,汪忠志.ĳ��ֵ��ʱCopula��Ž��Ⱥ�ṹ�Ϳ�խ��[J].应用概率统计,2014,30(1):12-22.

作者姓名：	徐付霞董永权汪忠志

作者单位：	???????????, ????????????????????, ???????????????

摘要：	本文证明了copula , 生存copula , 对偶copula 和伴随copula 关于copula的复合运算构成一个四元群, 给出了当某个单点值给定时它们的最优上下界. 计算了, 时copula最优上下界的宽窄度, 并与时的宽窄度进行了比较.
关键词：	???? Frechet-Hoeffding?? ???? /> ????? ?????.
Group Structure and Narrowing Effectiveness of Best-Possible Bounds for Copulas Specified at a Single Interior Point

Xu Fuxia,Dong Yongquan,Wang Zhongzhi.Group Structure and Narrowing Effectiveness of Best-Possible Bounds for Copulas Specified at a Single Interior Point[J].Chinese Journal of Applied Probability and Statisties,2014,30(1):12-22.

Authors:	Xu Fuxia Dong Yongquan Wang Zhongzhi

Institution:	School of Science, Tianjin Polytechnic University; Department of Mathematics and Information Science, Tangshan Normal University; School of Mathematics and Physics, Anhui University of Technology

Abstract:	We express the group structure of sets of a copula $\100dpi \inline $C(u,v)$$ , survival copula $\100dpi \inline $\wh{C}$$ , the dual of a copula $\100dpi \inline $\wt{C}$$ , and the co-copula $\100dpi \inline $C^*$$ , give the best-possible bounds for the last three functions where the value of every function is known at a single point. Especially, we find an general narrowing effectiveness coefficient $\100dpi \inline $m(\theta)$$ for $\100dpi \inline $C(a,b)=\theta$$ , compare the values of $\100dpi \inline $m(\theta)$$ where $\100dpi \inline $C(1/2,1/2)=\theta$$ to thoses for $\100dpi \inline $a,b$$ being other values in $\100dpi \inline $0,1]$$ .

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