Nonexchangeable Degrees of Best-Possible Bounds for Copulas Specified at a Single Interior Point
某个单点值给定的Copula最优界的不可交换性度量

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.