某个单点值给定的Copula最优界的不可交换性度量

通过研究某个单点值给定的Copula(相关结构函数)的最佳上下界的不可交换性度量,构造了4个奇异的Copula,它们具有最大的不可交换性,揭示了最大不可交换Copula的结构特点和性质.定义了非径向对称和非联合对称意义下的随机变量的不可交换性,指出对于4个最大不可交换的C叩ula,3种不可交换性度量是相同的.另一方面,研究了在一般的Lp距离定义下的不可交换性度量的计算公式,确定了其中的标准化系数kp=3p 1(p 1)p 2/4,特别地k1=27/2和k2=81的计算公式可以作为常用的不可交换性度量.

Nonexchangeable Degrees of Best-Possible Bounds for Copulas Specified at a Single Interior Point

The degrees of nonexchangeability about the best bounds of Copulas being specified at a single interior point are studied to construct four maximally nonexchangeable Copulas whose features and properties are studied as whell. Moreover this paper define non-radially and non-jointly symmetry about random variables and Copulas, and show that for the four Copulas the three nonexchangeable measures are equivelent. On the other hand, using $L_P$ distance theory we calculate another nonexchangeable degree formulate whose normal coefficient is k_p=3^{p+1}(p+1){{p+2} \over 4}, in particular, the formulate with k_1={27 \over 2} or k_2=81 may be commonly used.