# On the multivariate probability integral transformation

*Christian Genest* and
*Louis-Paul Rivest*

*Statistics & Probability Letters*, 2001, vol. 53, issue 4, 391-399

**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.

**Keywords:** Copula; Extreme; value; distribution; Kendall's; tau (search for similar items in EconPapers)

**Date:** 2001

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