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(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem

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  • Gery Geenens

    (School of Mathematics and Statistics, UNSW Sydney, Kensington, Sydney, NSW 2052, Australia)

Abstract

In this short communication, I share some personal thoughts on Sklar’s theorem and copulas after reading the original paper (Sklar, 1959) in French. After providing a literal translation of Sklar’s original statements, I argue that the modern version of ‘Sklar’s theorem’ given in most references has a slightly different emphasis, which may lead to subtly different interpretations. In particular, with no reference to the subcopula, modern ‘Sklar’s theorem’ does not provide the clues to fully appreciate when the copula representation of a distribution may form a valid basis for dependence modelling and when it may not.

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  • Gery Geenens, 2024. "(Re-)Reading Sklar (1959)—A Personal View on Sklar’s Theorem," Mathematics, MDPI, vol. 12(3), pages 1-7, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:380-:d:1325780
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    References listed on IDEAS

    as
    1. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    2. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
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