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Dependence Modeling

Ed. by Puccetti, Giovanni

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Emerging Science

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Online
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2300-2298
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An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem

Frank Oertel
  • Deloitte LLP, Audit - Banking & Capital Markets, Hill House, 1 Little New Street, London, EC4A 3TR, UK
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Published Online: 2015-09-09 | DOI: https://doi.org/10.1515/demo-2015-0008

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.

Keywords: Copulas, distributional transform; generalised inverse functions; Sklar’s Theorem

MSC:: 26A27; 60E05; 60A99; 62H05

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About the article


Received: 2015-03-11

Accepted: 2015-08-12

Published Online: 2015-09-09


Citation Information: Dependence Modeling, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2015-0008.

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© 2015 Frank Oertel. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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