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Dependence Modeling

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Maximum asymmetry of copulas revisited

Noppadon Kamnitui / Juan Fernández-Sánchez
  • Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain
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/ Wolfgang Trutschnig
Published Online: 2018-03-02 | DOI: https://doi.org/10.1515/demo-2018-0003


Motivated by the nice characterization of copulas A for which d(A, At) is maximal as established independently by Nelsen [11] and Klement & Mesiar [7], we study maximum asymmetry with respect to the conditioning-based metric D1 going back to Trutschnig [12]. Despite the fact that D1(A, At) is generally not straightforward to calculate, it is possible to provide both, a characterization and a handy representation of all copulas A maximizing D1(A, At). This representation is then used to prove the existence of copulas with full support maximizing D1(A, At). A comparison of D1- and d-asymmetry including some surprising examples rounds off the paper.

Keywords: Copula; exchangeability; symmetry; complete dependence; Markov kernel

MSC 2010: 60E05; 62E10; 28A12; 62H05


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About the article

Received: 2017-12-01

Accepted: 2018-01-31

Published Online: 2018-03-02

Citation Information: Dependence Modeling, Volume 6, Issue 1, Pages 47–62, ISSN (Online) 2300-2298, DOI: https://doi.org/10.1515/demo-2018-0003.

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© 2018, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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