某个单点值给定的Copula最优界的不可交换性度量

董永权;苏红顺;徐付霞

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (7) : 886-896.

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系统科学与数学 ›› 2008, Vol. 28 ›› Issue (7) : 886-896. DOI: 10.12341/jssms10194
论文

某个单点值给定的Copula最优界的不可交换性度量

    董永权(1), 苏红顺(2), 徐付霞(3)
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Nonexchangeable Degrees of Best-Possible Bounds for Copulas Specified at a Single Interior Point

    DONG Yongquan(1), SU Hongshun(2), XU Fuxia(3)
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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k_p=3^{p+1}(p+1){{p+2} \over 4},特别地k_1={27 \over 2}和k_2=81的计算公式可以作为常用的不可交换性度量.

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 LP 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.

关键词

相关结构函数 / 不可交换随机变量 / 界 / 相关系数 / 距离.

Key words

Copulas / nonexchangeable random variables / correlation coefficient / bounds / distance.

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董永权 , 苏红顺 , 徐付霞. 某个单点值给定的Copula最优界的不可交换性度量. 系统科学与数学, 2008, 28(7): 886-896. https://doi.org/10.12341/jssms10194
DONG Yongquan , SU Hongshun , XU Fuxia. Nonexchangeable Degrees of Best-Possible Bounds for Copulas Specified at a Single Interior Point. Journal of Systems Science and Mathematical Sciences, 2008, 28(7): 886-896 https://doi.org/10.12341/jssms10194
中图分类号： 60E15   
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