On the construction of minimum information bivariate copula families

Tim Bedford, Kevin J. Wilson

Research output: Contribution to journalArticle

10 Citations (Scopus)
210 Downloads (Pure)

Abstract

Copulas have become very popular as modelling tools in probability applications. Given a finite number of expectation constraints for functions defined on the unit square, the minimum information copula is that copula which has minimum information (Kullback-Leibler divergence) from the uniform copula. This can be considered the most ``independent'' copula satisfying the constraints. We demonstrate the existence and uniqueness of such copulas, rigorously establish the relation with discrete approximations, and prove an unexpected relationship between constraint expectation values and the copula density formula.
Original languageEnglish
Pages (from-to)703-723
Number of pages21
JournalAnnals of the Institute of Statistical Mathematics
Volume66
Issue number4
DOIs
Publication statusPublished - 21 Aug 2014

Keywords

  • bivariate copulas
  • information
  • uncertainty modelling
  • expert judgement

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