Open Access

Bounds for Trivariate Copulas with Given Bivariate Marginals

  • Fabrizio Durante1,
  • Erich Peter Klement1 and
  • José Juan Quesada-Molina2Email author
Journal of Inequalities and Applications20082008:161537

DOI: 10.1155/2008/161537

Received: 5 March 2008

Accepted: 26 September 2008

Published: 27 November 2008

Abstract

We determine two constructions that, starting with two bivariate copulas, give rise to new bivariate and trivariate copulas, respectively. These constructions are used to determine pointwise upper and lower bounds for the class of all trivariate copulas with given bivariate marginals.

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Authors’ Affiliations

(1)
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University
(2)
Departamento de Matemática Aplicada, Universidad de Granada

Copyright

© Fabrizio Durante et al. 2008

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.