一类新型单参数扰动Copula函数的构造和性质  

Construction and properties of a new one-parameter perturbation of Copula functions

作　　者：姚远[1] 徐付霞 YAO Yuan;XU Fu-xia(School of Mathematical Sciences,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学数学科学学院,天津300387

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第1期87-94,共8页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：证明了在一定条件下给定二元Copula函数增加扰动项之后仍是一个Copula函数,给出了单参数扰动Copula的和谐性度量τ和ρ的计算公式.以乘积Π_(λ),FGM_(θ)^(λ)为例探讨了τ和ρ随扰动参数的变化规律,拓展了原Copula的相关性度量范围,增强了适用性.对单点值给定的Copula的上下界C_(U),C_(L)增加扰动项构造新的奇异型Copula,并研究其和谐性度量和非对称性度量.It was proved that a given bivariate Copula function is still a Copula function after adding perturbed terms under certain conditions.The calculation formulas of two measures of concordance ofτandρfor a one-parameter perturbed Copula were given.Taking the products Π_(λ) and FGM_(θ)^(λ)as examples,the variation law of τ and ρ with perturbed parameters were discussed,which extended the correlation measurement range of original Copula and increases its applicability.A new singular Copula function was constructed by adding perturbed terms to the upper and lower bounds C_(U) and C_(L) of the Copula function with a given single point value,and its dependence measures and asymmetry measures were studied.

关 键 词：COPULA函数 单参数扰动 和谐性度量 不可交换性度量 最佳界 

分 类 号：O212.5[理学—概率论与数理统计]