关于对称Copula的一个注记  

A NOTE ON SYMMETRIC COPULA

作　　者：穆燕[1] 汪忠志[1] 

机构地区：[1]安徽工业大学数理学院,安徽马鞍山243002

出　　处：《数学杂志》2013年第6期1085-1092,共8页Journal of Mathematics

基　　金：国家自然科学基金资助(11071104);安徽工业大学青年基金(QZ2010018;Z11143);安徽工业大学研究生创新基金资助(D2011025)

摘　　要：本文研究了各种对称Copula的基本性质.利用构造具有二次与三次截线的Copula的方法,获得了具有左边块对称,但不是右边块对称;左边块对称、径向对称,但不是可交换;左边块对称,但既不是径向对称、也不是可交换的Copula.同时证明了不存在左边块对称、可交换,但不是径向对称的Copula,彻底解决了文献[2]中提出的四个问题.In this paper, we study the properties of various symmetry Coupulas. By using the way of constructing the Copula with quadratic sections or cubic sections, we obtain the family of Copulas which is Left-Block-Symmetry, not Right-Block-Symmetry, and the family of Copulas which is Left-Block-Symmetry and Radial-Symmetry but not exchangeable the family of Copulas which is Left-Block-Symmetry, but neither Radial-Symmetry, nor exchangeable. Meanwhile, we prove that the Copula, which is Left-Block-Symmetry, exchangeable and not Radial-Symmetry, does not exist. Therefore, the four problems proposed by Wang Qin in reference [2] are solved completely.

关 键 词：COPULA 对称Copula 可交换Copula 生存Copula 

分 类 号：O212.4[理学—概率论与数理统计]