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Copula modeling for discrete random vectors

Author

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  • Geenens Gery

    (School of Mathematics and Statistics, UNSW Sydney, Australia, tel +61 2 938 57032, fax +61 2 9385 7123)

Abstract

Copulas have now become ubiquitous statistical tools for describing, analysing and modelling dependence between random variables. Sklar’s theorem, “the fundamental theorem of copulas”, makes a clear distinction between the continuous case and the discrete case, though. In particular, the copula of a discrete random vector is not fully identifiable, which causes serious inconsistencies. In spite of this, downplaying statements may be found in the related literature, where copula methods are used for modelling dependence between discrete variables. This paper calls to reconsidering the soundness of copula modelling for discrete data. It suggests a more fundamental construction which allows copula ideas to smoothly carry over to the discrete case. Actually it is an attempt at rejuvenating some century-old ideas of Udny Yule, who mentioned a similar construction a long time before copulas got in fashion.

Suggested Citation

  • Geenens Gery, 2020. "Copula modeling for discrete random vectors," Dependence Modeling, De Gruyter, vol. 8(1), pages 417-440, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:417-440:n:16
    DOI: 10.1515/demo-2020-0022
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    References listed on IDEAS

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    Cited by:

    1. Rafał Wójcik & Charlie Wusuo Liu, 2022. "Bivariate Copula Trees for Gross Loss Aggregation with Positively Dependent Risks," Risks, MDPI, vol. 10(8), pages 1-24, July.

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