×

Transformations of copulas. (English) Zbl 1243.62019

Summary: Transformations of copulas by means of increasing bijections on the unit interval and attractors of copulas are discussed. The invariance of copulas under such transformations as well as the relationship to maximum attractors and Archimax copulas is investigated.

MSC:

62E15 Exact distribution theory in statistics
62H05 Characterization and structure theory for multivariate probability distributions; copulas
PDFBibTeX XMLCite
Full Text: EuDML Link

References:

[1] Aczél J., Alsina C.: Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. Methods Oper. Res. 48 (1984) 3-22 · Zbl 0527.39002
[2] Ali M. M., Mikhail N. N., Haq M. S.: A class of bivariate distributions including the bivariate logistic. J. Multivariate Anal. 8 (1978), 405-412 · Zbl 0387.62019 · doi:10.1016/0047-259X(78)90063-5
[3] Alsina C., Frank M. J., Schweizer B.: Associative Functions on Intervals: A Primer on Triangular Norms, in pres. · Zbl 1100.39023
[4] Calvo T., Mayor, G., (eds.) R. Mesiar: Aggregation Operators. New Trends and Applications. Physica-Verlag, Heidelberg 2002 · Zbl 0983.00020
[5] Capéraà P., Fougères A.-L., Genest C.: Bivariate distributions with given extreme value attractor. J. Multivariate Anal. 72 (2000), 30-49 · Zbl 0978.62043 · doi:10.1006/jmva.1999.1845
[6] Cuculescu I., Theodorescu R.: Extreme value attractors for star unimodal copulas. C. R. Math. Acad. Sci. Paris 334 (2002) 689-692 · Zbl 0996.60026 · doi:10.1016/S1631-073X(02)02322-1
[7] Galambos J.: The Asymptotic Theory of Extreme Order Statistics. Robert E. Krieger Publishing, Melbourne 1987 · Zbl 0634.62044
[8] Genest C., Rivest L.-P.: A characterization of Gumbel’s family of extreme value distributions. Statist. Probab. Lett. 8 (1989), 207-211 · Zbl 0701.62060 · doi:10.1016/0167-7152(89)90123-5
[9] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer, Dordrecht 2000 · Zbl 1087.20041 · doi:10.1017/S1446788700008065
[10] Klement E. P., Mesiar, R., Pap E.: Archimax copulas and invariance under transformations. C. R. Math. Acad. Sci. Paris 340 (2005), 755-758 · Zbl 1126.62040 · doi:10.1016/j.crma.2005.04.012
[11] Klir G. J., Folger T. A.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs, NJ 1988 · Zbl 0675.94025
[12] Mikusiński P., Taylor M. D.: A remark on associative copulas. Comment. Math. Univ. Carolin. 40 (1999), 789-793 · Zbl 1010.60014
[13] Nelsen R. B.: An Introduction to Copulas. (Lecture Notes in Statistics 139.) Springer, New York 1999 · Zbl 1152.62030 · doi:10.1007/978-1-4757-3076-0
[14] Pickands J.: Multivariate extreme value distributions. Bull. Inst. Internat. Statist. 49 (1981), 859-878 · Zbl 0518.62045
[15] Rückschlossová T.: Aggregation Operators and Invariantness. Ph.D. Thesis, Slovak University of Technology, Bratislava 2003
[16] Schweizer B., Sklar A.: Probabilistic Metric Spaces. North-Holland, New York 1983 · Zbl 0546.60010
[17] Sklar A.: Fonctions de répartition à \(n\) dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231 · Zbl 0100.14202
[18] Tawn J. A.: Bivariate extreme value theory: models and estimation. Biometrika 75 (1988), 397-415 · Zbl 0653.62045 · doi:10.1093/biomet/75.3.397
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.