A decomposition of copulas and its use

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In this article, we create a decomposition that represents and describes the depen-dence structure between two variables. Since copulas provide a deep understanding of the dependence structure by eliminating the effects of the marginals, they play a key role in this study. We define a discretized copula density matrix and decompose it into a set of permutation matrices by using the Birkhoff-von Neumann theorem. This decomposition provides a way to effectively apply the concepts of copulas to solve problems in multivariate statistical data analysis.

Original languageEnglish (US)
Pages (from-to)2269-2282
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Issue number12
StatePublished - Dec 1 2005


  • Birkhoff-von Neumann theorem
  • Copulas
  • Discretized copulas
  • Doubly stochastic matrix
  • Gini's measure
  • Permutation matrix
  • Prior probability


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