The Fréchet transform
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 constru...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000183 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |