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Communications in Statistics - Theory and Methods Volume 37, 2008 - Issue 18
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MULTIVARIATE ANALYSIS

Absolutely Continuous Copulas with Given Diagonal Sections

Fabrizio Durante Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, AustriaCorrespondence[email protected]
&
Piotr Jaworski Institute of Mathematics, Warsaw University, Warszawa, Poland
Pages 2924-2942 | Received 22 Jun 2007, Accepted 12 Mar 2008, Published online: 31 Jul 2008
 
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Abstract

Necessary and sufficient conditions are given in order to ensure that a function δ:[0, 1] → [0, 1] is the diagonal section of an absolutely continuous copula. Explicit constructions are provided.

Mathematics Subject Classification:

Acknowledgments

The authors are grateful to the Associate Editor and anonymous reviewers for their comments and useful suggestions. The first author acknowledges helpful discussions with Peter Sarkoci (Department of Knowledge-Based Mathematical Systems, Linz, Austria). This work was partially supported by the project “Copula Theory and its Applications”, bilateral cooperation Austria-Poland (WTZ, project PL 03/2008).

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