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.
出处
《烟台大学学报（自然科学与工程版）》
CAS
北大核心
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)
关键词
COPULA
反例
随机变量
独立
Copula
counterexample
random variable
independence
