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On the multivariate probability integral transformation

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  • Genest, Christian
  • Rivest, Louis-Paul

Abstract

A general formula is given for computing the distribution function K of the random variable H(X,Y) obtained by taking the bivariate probability integral transformation (BIPIT) of a random pair (X,Y) with distribution function H. Of particular interest is the behavior of the sequence (Kn) corresponding to the BIPIT of pairs (Xn,Yn) of componentwise maxima Xn=max(X1,...,Xn) and Yn=max(Y1, ..., Yn) of random samples (X1,Y1),...,(Xn,Yn) from distribution H. Illustrations are provided and the potential for statistical application is outlined. Multivariate extensions are briefly considered.

Suggested Citation

  • Genest, Christian & Rivest, Louis-Paul, 2001. "On the multivariate probability integral transformation," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 391-399, July.
    • Handle: RePEc:eee:stapro:v:53:y:2001:i:4:p:391-399
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    References listed on IDEAS

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    4. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    5. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
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