某个单点值给定时Copula最优界的群结构和宽窄度(英文)

Group Structure and Narrowing Effectiveness of Best-Possible Bounds for Copulas Specified at a Single Interior Point

本文证明了copWa C(u,υ),生存copula C,对偶copulaC和伴随copula C*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C(a,b)=θ,a,b∈[0,1]时copua最优上下界的宽窄度m(θ),并与C/2,1/2)=θ时的宽窄度进行了比较.

We express the group structure of sets of a copula C（u, v）, survival copula C, the dual of a copula C, and the co-copula 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 m（0） for C（a, b） = 0, compare the values of re（O） where C（1/2, 1/2） = 0 to thoses for a, b being other values in [0, 1].