Maximum asymmetry of copulas revisited

Noppadon Kamnitui 1 , Juan Fernández-Sánchez 2  and Wolfgang Trutschnig 1
  • 1 Department for Mathematics, University of Salzburg, , Salzburg, Austria
  • 2 Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, , Almería, Spain

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.

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Dependence Modeling aims to provide a medium for exchanging results and ideas in the area of multivariate dependence modeling. Topics include Copula methods, environmental sciences, estimation and goodness-of-fit tests, extreme-value theory, limit laws, mass transportations, measures of association, multivariate distributions and tests, quantitative risk management, risk assessment, risk models, risk measures and stochastic orders and time series.

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