Shuffles of Min.

Mikusinski, Piotr, Sherwood, Howard, and Taylor, Michael D.. "Shuffles of Min.." Stochastica 13.1 (1992): 61-74. <http://eudml.org/doc/39282>.

@article{Mikusinski1992,
abstract = {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.},
author = {Mikusinski, Piotr, Sherwood, Howard, Taylor, Michael D.},
journal = {Stochastica},
keywords = {Función cópula; Dependencia estocástica; Teoría de la distribución; Distribución marginal; doubly stochastic measure; functional dependence; stochastic independence; copulas; measure of dependence},
language = {eng},
number = {1},
pages = {61-74},
title = {Shuffles of Min.},
url = {http://eudml.org/doc/39282},
volume = {13},
year = {1992},
}

TY - JOUR
AU - Mikusinski, Piotr
AU - Sherwood, Howard
AU - Taylor, Michael D.
TI - Shuffles of Min.
JO - Stochastica
PY - 1992
VL - 13
IS - 1
SP - 61
EP - 74
AB - 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.
LA - eng
KW - Función cópula; Dependencia estocástica; Teoría de la distribución; Distribución marginal; doubly stochastic measure; functional dependence; stochastic independence; copulas; measure of dependence
UR - http://eudml.org/doc/39282
ER -