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Distribution functions of multivariate copulas

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  • Rodríguez-Lallena, José A.
  • Úbeda-Flores, Manuel

Abstract

For continuous random vectors X=(X1,X2,...,Xn) and multivariate distribution functions H1 and H2 with common univariate marginals, we study the distribution function of the random variable H1(X) given that the joint distribution function of X is H2. We show that the distribution function of H1(X) depends only on the copulas C1 and C2 associated with H1 and H2, and examine various properties of these distribution functions. We also illustrate some applications including multivariate dependence orderings.

Suggested Citation

  • Rodríguez-Lallena, José A. & Úbeda-Flores, Manuel, 2003. "Distribution functions of multivariate copulas," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 41-50, August.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:1:p:41-50
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    References listed on IDEAS

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    1. Genest, Christian & Rivest, Louis-Paul, 2001. "On the multivariate probability integral transformation," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 391-399, July.
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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.

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