基于Copula理论的随机变量的相关性

徐付霞,董永权,汪忠志

系统科学与数学 ›› 2012, Vol. 32 ›› Issue (4) : 485-495.

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PDF(335 KB)
系统科学与数学 ›› 2012, Vol. 32 ›› Issue (4) : 485-495. DOI: 10.12341/jssms11867
论文

基于Copula理论的随机变量的相关性

    徐付霞1,董永权2,汪忠志3
作者信息 +

DEPENDENCE OF RANDOM VARIABLES BASED ON COPULA THEORY

    XU Fuxia1,DONG Yongquan2,WANG Zhongzhi3
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文章历史 +

摘要

研究了用Copula表示的相关性度量σ相比于Pearsen线性相关系数r和和谐性度量τρ的优良性质,求解了4个最大不可交换Copula的相关性度量σ.为了便于计算,引入基于L2距离的相关性度量Φ,求解了某个单点值给定时Copula最优上下界的相关性度量ΦUΦL,作为特例,得到了4个最大不可交换Copula的另一种相关性度量Φ.

Abstract

This paper studies the superior properties of the dependence measure  ex- pressed with Copula comparing with Pearsen linear correlation coefficient r and the concordance measures  and , and obtains the dependence measures  of the four largest non-exchange Copulas. To make the calculation easier, another dependence measure  based on L2 distance is induced. The dependence measures U and L of Copula optimal upper and lower bounds at some single point value are given, and as a special case, the dependence measures  of the four largest non-commutative Copulas are given.

关键词

Copula / Spearman's ρ / Kendall's τ / 相关性度量σ / 相关性度量Φ.

Key words

Copula, Spearman&rsquo / s , Kendall&rsquo / s , dependence measure , dependence measure .

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徐付霞,董永权,汪忠志. 基于Copula理论的随机变量的相关性. 系统科学与数学, 2012, 32(4): 485-495. https://doi.org/10.12341/jssms11867
XU Fuxia,DONG Yongquan,WANG Zhongzhi. DEPENDENCE OF RANDOM VARIABLES BASED ON COPULA THEORY. Journal of Systems Science and Mathematical Sciences, 2012, 32(4): 485-495 https://doi.org/10.12341/jssms11867
中图分类号: 60E15   
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