Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each of which is almost surely an invertible function of the other such that X and X* are identically distributed as are Y and Y*. The preceding results shed light on A. Rényi's axioms for a measure of dependence and a modification of those axioms as given by B. Schweizer and E.F. Wolff.
@article{urn:eudml:doc:39282,
title = {Shuffles of Min.},
journal = {Stochastica},
volume = {13},
year = {1992},
pages = {61-74},
zbl = {0768.60017},
mrnumber = {MR1197328},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39282}
}
Mikusinski, Piotr; Sherwood, Howard; Taylor, Michael D. Shuffles of Min.. Stochastica, Tome 13 (1992) pp. 61-74. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39282/