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Distribution functions of copulas: a class of bivariate probability integral transforms

Author

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  • Nelsen, Roger B.
  • Quesada-Molina, José Juan
  • Rodríguez-Lallena, José Antonio
  • Úbeda-Flores, Manuel

Abstract

We discuss a two-dimensional analog of the probability integral transform for bivariate distribution functions H1 and H2, i.e., the distribution function of the random variable H1(X,Y) given that the joint distribution function of the random variables X and Y is H2. We study the case when H1 and H2 have the same continuous marginal distributions, showing that the distribution function of H1(X,Y) depends only on the copulas C1 and C2 associated with H1 and H2. We examine various properties of these "distribution functions of copulas", and illustrate applications including dependence orderings and measures of association.

Suggested Citation

  • Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2001. "Distribution functions of copulas: a class of bivariate probability integral transforms," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 277-282, October.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:3:p:277-282
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    Cited by:

    1. Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
    2. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
    3. Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2020. "Spearman's footrule and Gini's gamma: Local bounds for bivariate copulas and the exact region with respect to Blomqvist's beta," Papers 2009.06221, arXiv.org, revised Jan 2021.

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