Previous |  Up |  Next


Title: Orbital semilinear copulas (English)
Author: Jwaid, Tarad
Author: Baets, Bernard de
Author: Meyer, Hans de
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 45
Issue: 6
Year: 2009
Pages: 1012-1029
Summary lang: English
Category: math
Summary: We introduce four families of semilinear copulas (i.e. copulas that are linear in at least one coordinate of any point of the unit square) of which the diagonal and opposite diagonal sections are given functions. For each of these families, we provide necessary and sufficient conditions under which given diagonal and opposite diagonal functions can be the diagonal and opposite diagonal sections of a semilinear copula belonging to that family. We focus particular attention on the family of orbital semilinear copulas, which are obtained by linear interpolation on segments connecting the diagonal and opposite diagonal of the unit square. (English)
Keyword: copula
Keyword: diagonal section
Keyword: opposite diagonal section
Keyword: orbital semilinear copula
Keyword: semilinear copula
MSC: 62H05
MSC: 62H10
MSC: 62H20
idZBL: Zbl 1186.62067
idMR: MR2650080
Date available: 2010-06-02T19:33:07Z
Last updated: 2013-09-21
Stable URL:
Reference: [1] B. De Baets, H. De Meyer, and R. Mesiar: Asymmetric semilinear copulas.Kybernetika 43 (2007), 221–233. MR 2343397
Reference: [2] B. De Baets, H. De Meyer, and M. Úbeda-Flores: Opposite diagonal sections of quasi-copulas and copulas.Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 17 (2009), 481–490. MR 2591399
Reference: [3] B. De Baets, H. De Meyer, and M. Úbeda-Flores: Constructing copulas with given diagonal and opposite diagonal sections.Comm. Statist. – Theory Methods, to appear.
Reference: [4] F. Durante and P. Jaworski: Absolutely continuous copulas with given diagonal sections.Comm. Statist. – Theory Methods 37 (2008), 2924–2942. MR 2467742
Reference: [5] F. Durante, A. Kolesárová, R. Mesiar, and C. Sempi: Copulas with given diagonal sections, novel constructions and applications.Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 15 (2007), 397–410. MR 2362234
Reference: [6] F. Durante, A. Kolesárová, R. Mesiar, and C. Sempi: Semilinear copulas.Fuzzy Sets and Systems 159 (2008), 63–76. MR 2371303
Reference: [7] F. Durante, R. Mesiar, and C. Sempi: On a family of copulas constructed from the diagonal section.Soft Computing 10 (2006), 490–494.
Reference: [8] A. Erdely and J. M. González-Barrios: On the construction of families of absolutely continuous copulas with given restrictions.Comm. Statist. – Theory Methods 35 (2006), 649–659. MR 2282880
Reference: [9] P. Jaworski and T. Rychlik: On distributions of order statistics for absolutely continuous copulas with applications to reliability.Kybernetika 44 (2008), 757–776. MR 2488903
Reference: [10] H. Joe: Multivariate Models and Dependence Concepts.Chapman & Hall, London 1997. Zbl 0990.62517, MR 1462613
Reference: [11] E. Klement and A. Kolesárová: Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators.Kybernetika 43 (2005), 329–348. MR 2181422
Reference: [12] R. Nelsen: An Introduction to Copulas.Second edition. Springer, New York, 2006. Zbl 1152.62030, MR 2197664
Reference: [13] R. Nelsen and G. Fredricks: Diagonal copulas.In: Distributions with given Marginals and Moment Problems (V. Beneš and J. Štěpán, eds.), Kluwer Academic Publishers, Dordrecht 1977, pp. 121–127. MR 1614665
Reference: [14] R. Nelsen, J. Quesada-Molina, J. Rodríguez-Lallena, and M. Úbeda-Flores: On the construction of copulas and quasi-copula with given diagonal sections.Insurance: Math. Econ. 42 (2008), 473–483. MR 2404309
Reference: [15] A. Sklar: Fonctions de répartition à $n$ dimensions et leurs marges.Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231. MR 0125600
Reference: [16] M.-H. Zhang: Modelling total tail dependence along diagonals.Insurance: Math. Econ. 42 (2008), 73–80. Zbl 1142.62097, MR 2392071


Files Size Format View
Kybernetika_45-2009-6_10.pdf 971.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo