# Shuffles of Min.

Piotr Mikusinski; Howard Sherwood; Michael D. Taylor

Stochastica (1992)

- Volume: 13, Issue: 1, page 61-74
- ISSN: 0210-7821

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topMikusinski, 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 -

## Citations in EuDML Documents

top- Fabrizio Durante, Erich Peter Klement, José Quesada-Molina, Peter Sarkoci, Remarks on Two Product-like Constructions for Copulas
- Manuel Úbeda-Flores, Extreme distribution functions of copulas
- Noppadon Kamnitui, Tippawan Santiwipanont, Songkiat Sumetkijakan, Dependence Measuring from Conditional Variances

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