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On the construction of copulas and quasi-copulas with given diagonal sections

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  • Nelsen, Roger B.
  • Quesada-Molina, José Juan
  • Rodri­guez-Lallena, José Antonio
  • Úbeda-Flores, Manuel

Abstract

We study a method, which we call a copula (or quasi-copula) diagonal splice, for creating new functions by joining portions of two copulas (or quasi-copulas) with a common diagonal section. The diagonal splice of two quasi-copulas is always a quasi-copula, and we find a necessary and sufficient condition for the diagonal splice of two copulas to be a copula. Applications of this method include the construction of absolutely continuous asymmetric copulas with a prescribed diagonal section, and determining the best-possible upper bound on the set of copulas with a particular type of diagonal section. Several examples illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:2:p:473-483
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    5. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
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    2. 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(2013), pages 1-36, October.
    3. Cañón Salazar Carlos Iván, 2016. "Distributional Policy Effects with Many Treatment Outcomes," Working Papers 2016-01, Banco de México.
    4. Wysocki, Włodzimierz, 2012. "Constructing archimedean copulas from diagonal sections," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 818-826.
    5. Di Bernardino Elena & Rullière Didier, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-20, December.
    6. Elena Di Bernardino & Didier Rullière, 2015. "Estimation of multivariate critical layers: Applications to rainfall data," Post-Print hal-00940089, HAL.
    7. Beggs Alan W., 2013. "Dependence and Uniqueness in Bayesian Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 1-25, May.
    8. José Rodríguez-Lallena & Manuel Úbeda-Flores, 2010. "Multivariate copulas with quadratic sections in one variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 331-349, November.
    9. Juan Fernández Sánchez & Manuel Úbeda-Flores, 2014. "Semi-polynomial copulas," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 129-140, March.
    10. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    11. Elena Di Bernardino & Didier Rullière, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Working Papers hal-01147778, HAL.
    12. Butucea, Cristina & Delmas, Jean-François & Dutfoy, Anne & Fischer, Richard, 2015. "Maximum entropy copula with given diagonal section," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 61-81.
    13. Poulomi Ganguli & M. Reddy, 2012. "Risk Assessment of Droughts in Gujarat Using Bivariate Copulas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(11), pages 3301-3327, September.
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