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On the multivariate probability integral transformation

โœ Scribed by Christian Genest; Louis-Paul Rivest

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
112 KB
Volume
53
Category
Article
ISSN
0167-7152

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โœฆ Synopsis

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 brie y considered.

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