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Semi-polynomial copulas

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  • Juan Fernández Sánchez
  • Manuel Úbeda-Flores

Abstract

In this paper, we characterise a family of bivariate copulas whose sections between the main diagonal and the border of the unit square are polynomial, generalising several families of copulas, including those with quadratic and cubic sections. We also study a measure of association and the tail dependence for this class, illustrating our results with several examples.

Suggested Citation

  • Juan Fernández Sánchez & Manuel Úbeda-Flores, 2014. "Semi-polynomial copulas," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 129-140, March.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:1:p:129-140
    DOI: 10.1080/10485252.2013.839788
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    References listed on IDEAS

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    1. Rafael Schmidt & Ulrich Stadtmüller, 2006. "Non‐parametric Estimation of Tail Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 307-335, June.
    2. Alsina, Claudi & Nelsen, Roger B. & Schweizer, Berthold, 1993. "On the characterization of a class of binary operations on distribution functions," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 85-89, May.
    3. 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.
    4. 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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    Cited by:

    1. Zalzadeh, Saeed & Pellerey, Franco, 2016. "A positive dependence notion based on componentwise unimodality of copulas," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 51-57.

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