Keywords: copula; transformation of copulas; invariant copulas; maximum attractor; Archimax copula
@article{KYB_2005_41_4_a0,
author = {Klement, Erich Peter and Mesiar, Radko and Pap, Endre},
title = {Transformations of copulas},
journal = {Kybernetika},
pages = {425--434},
year = {2005},
volume = {41},
number = {4},
mrnumber = {2180355},
zbl = {1243.62019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_2005_41_4_a0/}
}
Klement, Erich Peter; Mesiar, Radko; Pap, Endre. Transformations of copulas. Kybernetika, Tome 41 (2005) no. 4, pp. 425-434. http://geodesic.mathdoc.fr/item/KYB_2005_41_4_a0/
[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 | Zbl
[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 | MR
[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 | Zbl
[5] Capéraà P., Fougères A.-L., Genest C.: Bivariate distributions with given extreme value attractor. J. Multivariate Anal. 72 (2000), 30–49 | DOI | MR | Zbl
[6] Cuculescu I., Theodorescu R.: Extreme value attractors for star unimodal copulas. C. R. Math. Acad. Sci. Paris 334 (2002) 689–692 | DOI | MR | Zbl
[7] Galambos J.: The Asymptotic Theory of Extreme Order Statistics. Robert E. Krieger Publishing, Melbourne 1987 | MR | Zbl
[8] Genest C., Rivest L.-P.: A characterization of Gumbel’s family of extreme value distributions. Statist. Probab. Lett. 8 (1989), 207–211 | DOI | MR | Zbl
[9] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer, Dordrecht 2000 | MR | Zbl
[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 | MR | Zbl
[11] Klir G. J., Folger T. A.: Fuzzy Sets, Uncertainty, and Information. Prentice Hall, Englewood Cliffs, NJ 1988 | MR | Zbl
[12] Mikusiński P., Taylor M. D.: A remark on associative copulas. Comment. Math. Univ. Carolin. 40 (1999), 789–793 | MR
[13] Nelsen R. B.: An Introduction to Copulas. (Lecture Notes in Statistics 139.) Springer, New York 1999 | DOI | MR | Zbl
[14] Pickands J.: Multivariate extreme value distributions. Bull. Inst. Internat. Statist. 49 (1981), 859–878 (with a discussion, 894–902) | MR | Zbl
[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 | Zbl
[17] Sklar A.: Fonctions de répartition à $n$ dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 | MR
[18] Tawn J. A.: Bivariate extreme value theory: models and estimation. Biometrika 75 (1988), 397–415 | DOI | MR | Zbl