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An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem

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  • Oertel Frank

    (Deloitte LLP, Audit - Banking & Capital Markets, Hill House, 1 Little New Street, London, EC4A 3TR, UK)

Abstract

We revisit Sklar’s Theorem and give another proof, primarily based on the use of right quantile functions. To this end we slightly generalise the distributional transform approach of Rüschendorf and facilitate some new results including a rigorous characterisation of an almost surely existing “left-invertibility” of distribution functions.

Suggested Citation

  • Oertel Frank, 2015. "An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-13, September.
    • Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:13:n:8
    DOI: 10.1515/demo-2015-0008
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    References listed on IDEAS

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    1. Paul Embrechts & Marius Hofert, 2013. "A note on generalized inverses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 423-432, June.
    2. Ahmed, Shabbir & Cakmak, Ulas & Shapiro, Alexander, 2007. "Coherent risk measures in inventory problems," European Journal of Operational Research, Elsevier, vol. 182(1), pages 226-238, October.
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    Cited by:

    1. Šeliga Adam & Kauers Manuel & Saminger-Platz Susanne & Mesiar Radko & Kolesárová Anna & Klement Erich Peter, 2021. "Polynomial bivariate copulas of degree five: characterization and some particular inequalities," Dependence Modeling, De Gruyter, vol. 9(1), pages 13-42, January.
    2. Saminger-Platz Susanne & Kolesárová Anna & Šeliga Adam & Mesiar Radko & Klement Erich Peter, 2021. "New results on perturbation-based copulas," Dependence Modeling, De Gruyter, vol. 9(1), pages 347-373, January.

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