Maximal asymmetry of bivariate copulas and consequences to measures of dependence
In this article, we focus on copulas underlying maximal non-exchangeable pairs (X,Y)\left(X,Y) of continuous random variables X,YX,Y either in the sense of the uniform metric d∞{d}_{\infty } or the conditioning-based metrics Dp{D}_{p}, and analyze their possible extent of dependence quantified by th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2022-08-01
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| Series: | Dependence Modeling |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/demo-2022-0115 |
| _version_ | 1811236542735187968 |
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| author | Griessenberger Florian Trutschnig Wolfgang |
| author_facet | Griessenberger Florian Trutschnig Wolfgang |
| author_sort | Griessenberger Florian |
| collection | DOAJ |
| description | In this article, we focus on copulas underlying maximal non-exchangeable pairs (X,Y)\left(X,Y) of continuous random variables X,YX,Y either in the sense of the uniform metric d∞{d}_{\infty } or the conditioning-based metrics Dp{D}_{p}, and analyze their possible extent of dependence quantified by the recently introduced dependence measures ζ1{\zeta }_{1} and ξ\xi . Considering maximal d∞{d}_{\infty }-asymmetry we obtain ζ1∈56,1{\zeta }_{1}\in \left[\frac{5}{6},1\right] and ξ∈23,1\xi \in \left[\frac{2}{3},1\right], and in the case of maximal D1{D}_{1}-asymmetry we obtain ζ1∈34,1{\zeta }_{1}\in \left[\frac{3}{4},1\right] and ξ∈12,1\xi \in \left(\frac{1}{2},1\right], implying that maximal asymmetry implies a very high degree of dependence in both cases. Furthermore, we study various topological properties of the family of copulas with maximal D1{D}_{1}-asymmetry and derive some surprising properties for maximal Dp{D}_{p}-asymmetric copulas. |
| first_indexed | 2024-04-12T12:09:58Z |
| format | Article |
| id | doaj.art-47e7ac96982043d2ab009367aa19c41c |
| institution | Directory Open Access Journal |
| issn | 2300-2298 |
| language | English |
| last_indexed | 2024-04-12T12:09:58Z |
| publishDate | 2022-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Dependence Modeling |
| spelling | doaj.art-47e7ac96982043d2ab009367aa19c41c2022-12-22T03:33:36ZengDe GruyterDependence Modeling2300-22982022-08-0110124526910.1515/demo-2022-0115Maximal asymmetry of bivariate copulas and consequences to measures of dependenceGriessenberger Florian0Trutschnig Wolfgang1Department for Artificial Intelligence and Human Interfaces, University of Salzburg, Hellbrunnerstrasse 34, 5020 Salzburg, AustriaDepartment for Artificial Intelligence and Human Interfaces, University of Salzburg, Hellbrunnerstrasse 34, 5020 Salzburg, AustriaIn this article, we focus on copulas underlying maximal non-exchangeable pairs (X,Y)\left(X,Y) of continuous random variables X,YX,Y either in the sense of the uniform metric d∞{d}_{\infty } or the conditioning-based metrics Dp{D}_{p}, and analyze their possible extent of dependence quantified by the recently introduced dependence measures ζ1{\zeta }_{1} and ξ\xi . Considering maximal d∞{d}_{\infty }-asymmetry we obtain ζ1∈56,1{\zeta }_{1}\in \left[\frac{5}{6},1\right] and ξ∈23,1\xi \in \left[\frac{2}{3},1\right], and in the case of maximal D1{D}_{1}-asymmetry we obtain ζ1∈34,1{\zeta }_{1}\in \left[\frac{3}{4},1\right] and ξ∈12,1\xi \in \left(\frac{1}{2},1\right], implying that maximal asymmetry implies a very high degree of dependence in both cases. Furthermore, we study various topological properties of the family of copulas with maximal D1{D}_{1}-asymmetry and derive some surprising properties for maximal Dp{D}_{p}-asymmetric copulas.https://doi.org/10.1515/demo-2022-0115asymmetrycopuladependence measureexchangeabilitymarkov kernel62h0562h2060e0554e52 |
| spellingShingle | Griessenberger Florian Trutschnig Wolfgang Maximal asymmetry of bivariate copulas and consequences to measures of dependence Dependence Modeling asymmetry copula dependence measure exchangeability markov kernel 62h05 62h20 60e05 54e52 |
| title | Maximal asymmetry of bivariate copulas and consequences to measures of dependence |
| title_full | Maximal asymmetry of bivariate copulas and consequences to measures of dependence |
| title_fullStr | Maximal asymmetry of bivariate copulas and consequences to measures of dependence |
| title_full_unstemmed | Maximal asymmetry of bivariate copulas and consequences to measures of dependence |
| title_short | Maximal asymmetry of bivariate copulas and consequences to measures of dependence |
| title_sort | maximal asymmetry of bivariate copulas and consequences to measures of dependence |
| topic | asymmetry copula dependence measure exchangeability markov kernel 62h05 62h20 60e05 54e52 |
| url | https://doi.org/10.1515/demo-2022-0115 |
| work_keys_str_mv | AT griessenbergerflorian maximalasymmetryofbivariatecopulasandconsequencestomeasuresofdependence AT trutschnigwolfgang maximalasymmetryofbivariatecopulasandconsequencestomeasuresofdependence |