When a copula is archimax
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.
Volume (Year): 83 (2013)
Issue (Month): 1 ()
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- Charpentier, Arthur & Segers, Johan, 2008.
"Convergence of Archimedean copulas,"
Statistics & Probability Letters,
Elsevier, vol. 78(4), pages 412-419, March.
- Charpentier, A. & Segers, J.J.J., 2006. "Convergence of Archimedean Copulas," Discussion Paper 2006-28, Tilburg University, Center for Economic Research.
- 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.
- Wysocki, Włodzimierz, 2012. "Constructing archimedean copulas from diagonal sections," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 818-826. Full references (including those not matched with items on IDEAS)
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