On the multivariate probability integral transformation
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.
Volume (Year): 53 (2001)
Issue (Month): 4 (July)
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- Barbe, Philippe & Genest, Christian & Ghoudi, Kilani & Rémillard, Bruno, 1996. "On Kendall's Process," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 197-229, August.
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