Piotor Mikusiński, Morgan Phillips, Howard Sherwood, Michael D. Taylor, "The Fréchet transform", International Journal of Mathematics and Mathematical Sciences, vol. 16, Article ID 291508, 10 pages, 1993. https://doi.org/10.1155/S0161171293000183
The Fréchet transform
Let be -dimensional probability distribution functions and be an -copula. Define an -dimensional probability distribution function by . Let , be the probability measure induced on by and be the probability measure induced on by . We construct a certain transformation of subsets of to subsets of 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 -tuples of random variables, but no applications are presented in this paper.
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