In:
International Journal of Mathematics and Mathematical Sciences, Hindawi Limited, Vol. 16, No. 1 ( 1993), p. 155-164
Abstract:
Let F 1 , … , F N be 1 -dimensional probability distribution functions and C be an N -copula. Define an N -dimensional probability distribution function G by G ( x 1 , … , x N ) = C ( F 1 ( x 1 ) , … , F N ( x N ) ) . Let ν , be the probability measure induced on ℝ N by G and μ be the probability measure induced on [ 0 , 1 ] N by C . We construct a certain transformation Φ of subsets of ℝ N 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.
Type of Medium:
Online Resource
ISSN:
0161-1712
,
1687-0425
DOI:
10.1155/S0161171293000183
Language:
English
Publisher:
Hindawi Limited
Publication Date:
1993
detail.hit.zdb_id:
1492203-4
SSG:
17,1
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