Maximum asymmetry of copulas revisited

Kamnitui Noppadon (), Fernández-Sánchez Juan () and Trutschnig Wolfgang ()
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Kamnitui Noppadon: Department for Mathematics, University of Salzburg, Salzburg, Austria
Fernández-Sánchez Juan: Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain
Trutschnig Wolfgang: Department for Mathematics, University of Salzburg, Salzburg, Austria

Dependence Modeling, 2018, vol. 6, issue 1, 47-62

Abstract: 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 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:6:y:2018:i:1:p:47-62:n:3

DOI: 10.1515/demo-2018-0003

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