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When a copula is archimax

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  • Wysocki, Włodzimierz

Abstract

We discuss necessary and sufficient conditions for a copula to be archimax. We give a differential equation (depending on a function parameter) whose solution gives an additive generator of an Archimedean copula. We present two important applications of this differential equation. The first concerns the surprising fact that every Archimedean copula induces an uncountable family of such copulas. The other application is to a construction of Archimedean copulas from functions having the properties of opposite diagonal sections of Archimedean copulas.

Suggested Citation

  • Wysocki, Włodzimierz, 2013. "When a copula is archimax," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 37-45.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:37-45
    DOI: 10.1016/j.spl.2012.09.003
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    References listed on IDEAS

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    1. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    2. Wysocki, Włodzimierz, 2012. "Constructing archimedean copulas from diagonal sections," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 818-826.
    3. Charpentier, Arthur & Segers, Johan, 2008. "Convergence of Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 412-419, March.
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