Geodesic
Bivariate copulas: Transformations, asymmetry and measures of concordance
Kybernetika, Tome 50 (2014) no. 1, pp. 109-125 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the order between two copulas and the value of every measure of concordance.
The present paper introduces a group of transformations on the collection of all bivariate copulas. This group contains an involution which is particularly useful since it provides (1) a criterion under which a given symmetric copula can be transformed into an asymmetric one and (2) a condition under which for a given copula the value of every measure of concordance is equal to zero. The group also contains a subgroup which is of particular interest since its four elements preserve symmetry, the order between two copulas and the value of every measure of concordance.
DOI : 10.14736/kyb-2014-1-0109
Classification : 20C99, 60B15, 60E05, 62E10, 62H20
Keywords: bivariate copulas; transformations; asymmetry; measures of concordance 
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Fuchs, Sebastian; Schmidt, Klaus D. Bivariate copulas: Transformations, asymmetry and measures of concordance. Kybernetika, Tome 50 (2014) no. 1, pp. 109-125. doi: 10.14736/kyb-2014-1-0109

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