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Sibuya copulas

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  • Hofert, Marius
  • Vrins, Frédéric

Abstract

A new class of copulas referred to as “Sibuya copulas” is introduced and its properties are investigated. Members of this class are of a functional form which was first investigated in the work of M. Sibuya. The construction of Sibuya copulas is based on an increasing stochastic process whose Laplace–Stieltjes transform enters the copula as a parameter function. Sibuya copulas also allow for idiosyncratic parameter functions and are thus quite flexible to model asymmetric dependences. If the stochastic process is allowed to have jumps, Sibuya copulas may have a singular component. Depending on the choice of the process, they may be extreme-value copulas, Lévy-frailty copulas, or Marshall–Olkin copulas. Further, as a special symmetric case, one may obtain any Archimedean copula with Laplace–Stieltjes transform as generator. Besides some general properties of Sibuya copulas, several examples are given and their properties are investigated in more detail.

Suggested Citation

  • Hofert, Marius & Vrins, Frédéric, 2013. "Sibuya copulas," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 318-337.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:318-337
    DOI: 10.1016/j.jmva.2012.08.007
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    References listed on IDEAS

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    1. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    2. Masaaki Sibuya, 1959. "Bivariate extreme statistics, I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 11(2), pages 195-210, June.
    3. Frahm, Gabriel, 2006. "On the extremal dependence coefficient of multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1470-1481, August.
    4. Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
    5. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
    6. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
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    Cited by:

    1. Arbel, Julyan & Crispino, Marta & Girard, Stéphane, 2019. "Dependence properties and Bayesian inference for asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Su, Jianxi & Hua, Lei, 2017. "A general approach to full-range tail dependence copulas," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 49-64.
    3. Philipp Arbenz & Mathieu Cambou & Marius Hofert, 2014. "An importance sampling approach for copula models in insurance," Papers 1403.4291, arXiv.org, revised Apr 2015.

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