Transformations of copulas

Kybernetika

Volumn 41, Issue 4, 2005, Pages 425-434

  Klement, Erich Peter ^a   Mesiar, Radko ^b,c   Pap, Endre ^d  

^a JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^c INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

^d UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Archimax copula; Copula; Invariant copulas; Maximum attractor; Transformation of copulas

Indexed keywords

EID: 29144533856     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. J. Aczél and C. Alsina: Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. Methods Oper. Res. 48 (1984) 3-22.
2. M. M. Ali, N. N. Mikhail, and M. S. Haq: A class of bivariate distributions including the bivariate logistic. J. Multivariate Anal. 8 (1978), 405-412.
3. C. Alsina, M. J. Frank, and B. Schweizer: Associative Functions on Intervals: A Primer on Triangular Norms, in press.
4. T. Calvo, G. Mayor, and R. Mesiar (eds.): Aggregation Operators. New Trends and Applications. Physica-Verlag, Heidelberg 2002.
5. P. Capéraà, A.-L. Fougères, and C. Genest: Bivariate distributions with given extreme value attractor. J. Multivariate Anal. 72 (2000), 30-49.
6. I. Cuculescu and R. Theodorescu: Extreme value attractors for star unimodal copulas. C. R. Math. Acad. Sci. Paris 334 (2002) 689-692.
7. J. Galambos: The Asymptotic Theory of Extreme Order Statistics. Robert E. Krieger Publishing, Melbourne 1987.
8. C. Genest and L.-P. Rivest: A characterization of Gumbel's family of extreme value distributions. Statist. Probab. Lett. 8 (1989), 207-211.
9. E. P. Klement, R. Mesiar, and E. Pap: Triangular Norms. Kluwer, Dordrecht 2000.
10. E. P. Klement, R. Mesiar, and E. Pap: Archimax copulas and invariance under transformations. C.R. Math. Acad. Sci. Paris 340 (2005), 755-758.
11. G. J. Klir and T.A. Folger: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs, NJ 1988.
12. P. Mikusiński and M. D. Taylor: A remark on associative copulas. Comment. Math. Univ. Carolin. 40 (1999), 789-793.
13. R. B. Nelsen: An Introduction to Copulas. (Lecture Notes in Statistics 139.) Springer, New York 1999.
14. J. Pickands: Multivariate extreme value distributions. Bull. Inst. Internat. Statist. 49 (1981), 859-878 (with a discussion, 894-902).
15. T. Rückschlossová: Aggregation Operators and Invariantness. Ph.D. Thesis, Slovak University of Technology, Bratislava 2003.
16. B. Schweizer and A. Sklar: Probabilistic Metric Spaces. North-Holland, New York 1983.
17. A. Sklar: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231.
18. J. A. Tawn: Bivariate extreme value theory: models and estimation. Biometrika 75 (1988), 397-415.