基于Copula的一个概率论反例的构造  

Construction of a Counterexample in Probability Theory Based on Copula

作　　者：刘存霞[1] 

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2009年第2期93-96,共4页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：山东省软科学研究资助项目(B2006069)

摘　　要：Copula是描述随机变量间相关性的一个有力工具.利用Copula来构造概率论中有关随机变量的独立性的反例.首先以3-Copula为例构造了一个Copula族,继而通过这个Copula族,构造出随机变量X,Y,Z的联合分布函数,使得随机变量X,Y,Z中的任意2个都是独立的,但X,Y,Z不是相互独立的;最后通过例子说明,该方法较传统方法更为简洁有效.进一步地,这一方法可以应用到更高维数的场合.As a powerful tool to describe the correlation of random variables, Copula will be used in this paper to construct a counterexample about the independence of random variables. A family of 3-Copula is established firstly as an example. Then, based on the family of Copulas, the joint distribution function of random variables X, Y and Z is obtained such that X, Y and Z are pairwise independent but not mutually independent. The method used in this paper is simpler and more efficient than the classical way. Furthermore, the method can be applied to higher dimensional cases.

关 键 词：COPULA 反例 随机变量 独立 

分 类 号：O211.5[理学—概率论与数理统计]