期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1993
卷号：16
DOI：10.1155/S0161171293000183
出版社：Hindawi Publishing Corporation
摘要：Let F1,…,FN be 1-dimensional probability distribution functions and C be an N-copula.
Define an N-dimensional probability distribution function G by G(x1,…,xN)=C(F1(x1),…,FN(xN)). Let ν, be the probability measure induced on ℝN by G and μ be the
probability measure induced on [0,1]N by C. We construct a certain transformation Φ of subsets of
ℝN to subsets of [0,1]N which we call the Fréchet transform and prove that it is measure-preserving.
It is intended that this transform be used as a tool to study the types of dependence
which can exist between pairs or N-tuples of random variables, but no applications are presented in
this paper.
