Shuffles of Min.

• Autores: Piotr Mikusinski, Howard Sherwood, Michael Taylor
• Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 13, Nº. 1, 1992, págs. 61-74
• Idioma: inglés
• Títulos paralelos:
  • Cópulas de Min.
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• Resumen

  • 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.