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

✍ Scribed by Roger B. Nelsen; José Juan Quesada-Molina; José Antonio Rodrı́guez-Lallena; Manuel Úbeda-Flores

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
103 KB
Volume
54
Category
Article
ISSN
0167-7152

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✦ Synopsis

We discuss a two-dimensional analog of the probability integral transform for bivariate distribution functions H1 and H2, i.e., the distribution function of the random variable H1(X; Y ) given that the joint distribution function of the random variables X and Y is H2. We study the case when H1 and H2 have the same continuous marginal distributions, showing that the distribution function of H1(X; Y ) depends only on the copulas C1 and C2 associated with H1 and H2. We examine various properties of these "distribution functions of copulas", and illustrate applications including dependence orderings and measures of association.

📜 SIMILAR VOLUMES

Distribution functions of multivariate c
Distribution functions of multivariate copulas
✍ José A. Rodrı́guez-Lallena; Manuel Úbeda-Flores 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 239 KB

For continuous random vectors X = (X 1 ; X 2 ; : : : ; X n ) and multivariate distribution functions H 1 and H 2 with common univariate marginals, we study the distribution function of the random variable H 1 (X) given that the joint distribution function of X is H 2 . We show that the distribution