Distribution functions of copulas: a class of bivariate probability integral transforms

We discuss a two-dimensional analog of the probability integral transform for bivariate distribution functions H 1 and H 2, i.e., the distribution function of the random variable H 1( X, Y) given that the joint distribution function of the random variables X and Y is H 2. We study the case when H 1...

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Bibliographic Details
Published in:Statistics & probability letters 2001-10, Vol.54 (3), p.277-282
Main Authors: Nelsen, Roger B., Quesada-Molina, José Juan, Rodrı́guez-Lallena, José Antonio, Úbeda-Flores, Manuel
Format: Article
Language:English
Subjects:
Copulas
Copulas Dependence orderings Distribution functions Measures of association Probability integral transform
Dependence orderings
Distribution functions
Distribution theory
Exact sciences and technology
Mathematics
Measures of association
Multivariate analysis
Probability and statistics
Probability integral transform
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
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Summary:We discuss a two-dimensional analog of the probability integral transform for bivariate distribution functions H 1 and H 2, i.e., the distribution function of the random variable H 1( X, Y) given that the joint distribution function of the random variables X and Y is H 2. We study the case when H 1 and H 2 have the same continuous marginal distributions, showing that the distribution function of H 1( X, Y) depends only on the copulas C 1 and C 2 associated with H 1 and H 2. We examine various properties of these “distribution functions of copulas”, and illustrate applications including dependence orderings and measures of association.
ISSN:0167-7152
1879-2103
DOI:10.1016/S0167-7152(01)00060-8