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

Received: 5 March 2008

Accepted: 26 September 2008

Published: 27 November 2008


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

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


© 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.