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Constructing archimedean copulas from diagonal sections

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  • Wysocki, Włodzimierz

Abstract

We introduce a family ℱ of functions called diagonal generators. These are convex functions with the properties of diagonal sections of archimedean copulas. We show that to each diagonal generator f there corresponds an archimedean copula Cf with the asymptotic representation Cf(u1,u2)=limk→∞fk[f−k(u1)+f−k(u2)−1]. Moreover, the diagonal section of Cf equals f.

Suggested Citation

  • Wysocki, Włodzimierz, 2012. "Constructing archimedean copulas from diagonal sections," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 818-826.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:4:p:818-826
    DOI: 10.1016/j.spl.2012.01.008
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    References listed on IDEAS

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    1. Charpentier, Arthur & Segers, Johan, 2008. "Convergence of Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 412-419, March.
    2. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodri­guez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2008. "On the construction of copulas and quasi-copulas with given diagonal sections," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 473-483, April.
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    Cited by:

    1. Abdulhamid A. Alzaid & Weaam M. Alhadlaq, 2023. "A New Family of Archimedean Copulas: The Half-Logistic Family of Copulas," Mathematics, MDPI, vol. 12(1), pages 1-18, December.
    2. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    3. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1, pages 1-36, October.
    4. Elena Di Bernardino & Didier Rullière, 2015. "Estimation of multivariate critical layers: Applications to rainfall data," Post-Print hal-00940089, HAL.
    5. Wysocki, Włodzimierz, 2013. "When a copula is archimax," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 37-45.
    6. Schwarz, Maik & Jongbloed, Geurt & Van Keilegom, Ingrid, 2012. "On the identifiability of copulas in bivariate competing risks models," LIDAM Discussion Papers ISBA 2012032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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