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On the construction of minimum information bivariate copula families

Author

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  • Tim Bedford
  • Kevin Wilson

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. Copyright The Institute of Statistical Mathematics, Tokyo 2014

Suggested Citation

  • Tim Bedford & Kevin Wilson, 2014. "On the construction of minimum information bivariate copula families," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 703-723, August.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:4:p:703-723
    DOI: 10.1007/s10463-013-0422-0
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    Cited by:

    1. Tim Bedford & Alireza Daneshkhah & Kevin J. Wilson, 2016. "Approximate Uncertainty Modeling in Risk Analysis with Vine Copulas," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 792-815, April.
    2. Christoph Werner & Tim Bedford & John Quigley, 2018. "Sequential Refined Partitioning for Probabilistic Dependence Assessment," Risk Analysis, John Wiley & Sons, vol. 38(12), pages 2683-2702, December.

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