【摘要】 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Copula,3种不可交换性度量是相同的.另一方面,研究了在一般的L_P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k_p=3^p+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.更多还原

【Abstract】 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）/4,in particular,the formulate with k₁=（27）/2 or k₂=81 may be commonly used.更多还原