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Keywords:
copula; transformation of copulas; invariant copulas; maximum attractor; Archimax copula
copula; transformation of copulas; invariant copulas; maximum attractor; Archimax copula
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.
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 MR 0736352 | 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 DOI 10.1016/0047-259X(78)90063-5 | MR 0512610
[3] Alsina C., Frank M. J., Schweizer B.: Associative Functions on Intervals: A Primer on Triangular Norms, in pres.
[4] Calvo T., Mayor, G., (eds.) R. Mesiar: Aggregation Operators. New Trends and Applications. Physica–Verlag, Heidelberg 2002 MR 1936383 | 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 DOI 10.1006/jmva.1999.1845 | MR 1747422 | Zbl 0978.62043
[6] Cuculescu I., Theodorescu R.: Extreme value attractors for star unimodal copulas. C. R. Math. Acad. Sci. Paris 334 (2002) 689–692 DOI 10.1016/S1631-073X(02)02322-1 | MR 1903371 | Zbl 0996.60026
[7] Galambos J.: The Asymptotic Theory of Extreme Order Statistics. Robert E. Krieger Publishing, Melbourne 1987 MR 0936631 | 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 DOI 10.1016/0167-7152(89)90123-5 | MR 1024029 | Zbl 0701.62060
[9] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[10] Klement E. P., Mesiar, R., Pap E.: Archimax copulas and invariance under transformations. C. R. Math. Acad. Sci. Paris 340 (2005), 755–758 DOI 10.1016/j.crma.2005.04.012 | MR 2141065 | Zbl 1126.62040
[11] Klir G. J., Folger T. A.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs, NJ 1988 MR 0930102 | Zbl 0675.94025
[12] Mikusiński P., Taylor M. D.: A remark on associative copulas. Comment. Math. Univ. Carolin. 40 (1999), 789–793 MR 1756554
[13] Nelsen R. B.: An Introduction to Copulas. (Lecture Notes in Statistics 139.) Springer, New York 1999 DOI 10.1007/978-1-4757-3076-0 | MR 1653203 | Zbl 1152.62030
[14] Pickands J.: Multivariate extreme value distributions. Bull. Inst. Internat. Statist. 49 (1981), 859–878 (with a discussion, 894–902) MR 0820979 | 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 MR 0790314 | Zbl 0546.60010
[17] Sklar A.: Fonctions de répartition à $n$ dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 MR 0125600
[18] Tawn J. A.: Bivariate extreme value theory: models and estimation. Biometrika 75 (1988), 397–415 DOI 10.1093/biomet/75.3.397 | MR 0967580 | Zbl 0653.62045
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