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| 基于Copula理论的随机变量的相关性 | |
| 引用本文： | 徐付霞,董永权,汪忠志.基于Copula理论的随机变量的相关性[J].系统科学与数学,2012,32(4):485-495. |
| 作者姓名： | 徐付霞 董永权 汪忠志 |
| 作者单位： | 1. 天津工业大学理学院,天津,300387 2. 唐山师范学院数学与信息科学系,唐山,063000 3. 安徽工业大学数理学院,马鞍山,243002 |
| 基金项目： | 国家自然科学基金(11071104);河北省教育厅自然科学基金(Z2010322);唐山市科技局软科学基金(11140208a)资助课题 |
| 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τ与ρ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φU和φL,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. |
| 关 键 词： | Copula Spearman's ρ Kendall's τ 相关性度量σ 相关性度量φ |
DEPENDENCE OF RANDOM VARIABLES BASED ON COPULA THEORY |
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| XU Fuxia , DONG Yongquan , WANG Zhongzhi.DEPENDENCE OF RANDOM VARIABLES BASED ON COPULA THEORY[J].Journal of Systems Science and Mathematical Sciences,2012,32(4):485-495. | |
| Authors: | XU Fuxia DONG Yongquan WANG Zhongzhi |
| Institution: | (School of Mathematics and Physics,Anhui University of Technology,Ma’anshan 243002) |
| Abstract: | This paper studies the superior properties of the dependence measureσexpressed with Copula comparing with Pearsen linear correlation coefficientτand the concordance measuresτandρ,and obtains the dependence measuresσof the four largest non-exchange Copulas.To make the calculation easier,another dependence measureΦbased on L2 distance is induced.The dependence measuresΦU andΦl of Copula optimal upper and lower bounds at some single point value are given,and as a special case,the dependence measuresΦof the four largest non-commutative Copulas are given. |
| Keywords: | Copula Spearman’s ρ Kendall’s т dependence measure σ dependence measure Φ |
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