Title

The Fréchet Transform

Keywords

copula; distributions with fixed marginals; doubly stochastic measure; Fréchet transform; probability distribution function

Abstract

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 v 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,l]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. © 1993, Hindawi Publishing Corporation. All rights reserved.

Publication Date

1-1-1993

Publication Title

International Journal of Mathematics and Mathematical Sciences

Volume

16

Issue

1

Number of Pages

155-164

Document Type

Article

Identifier

scopus

Personal Identifier

scopus

DOI Link

https://doi.org/10.1155/S0161171293000183

Socpus ID

84968972996 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84968972996

This document is currently not available here.

Share

COinS