zbMATH — the first resource for mathematics

Asymmetric semilinear copulas. (English) Zbl 1136.62350
Summary: We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by \(1/16\). The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of \(\Pi\) and \(M\).

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H10 Multivariate distribution of statistics
62H20 Measures of association (correlation, canonical correlation, etc.)
Full Text: Link EuDML
[1] Bertino S.: On dissimilarity between cyclic permutations. Metron 35 (1977), 53-88, in Italian
[2] Durante F., Mesiar, R., Sempi C.: On a family of copulas constructed from the diagonal section. Soft Computing 10 (2006), 490-494 · Zbl 1098.60016 · doi:10.1007/s00500-005-0523-7
[3] Durante F., Kolesárová A., Mesiar, R., Sempi C.: Semilinear copulas. Submitted · Zbl 1274.62108 · doi:10.1016/j.fss.2007.09.001
[4] Durante F., Kolesárová A., Mesiar, R., Sempi C.: Copulas with given diagonal sections: novel constructions and applications. Submitted · Zbl 1158.62324 · doi:10.1142/S0218488507004753
[5] Joe H.: Multivariate Models and Dependence Concepts. Chapman & Hall, London 1997 · Zbl 0990.62517
[6] Klement E. P., Kolesárová A.: Extensions to copulas and quasi-copulas as special 1-Lipschitz aggregation operators. Kybernetika 41 (2005), 329-348 · Zbl 1249.60017 · www.kybernetika.cz · eudml:33757
[7] Klement E. P., Mesiar R.: How non-symmetric can a copula be? Comment. Math. Univ. Carolinae 47 (2006), 141-148 · Zbl 1150.62027 · emis:journals/CMUC/cmuc0601/cmuc0601.htm · eudml:22872
[8] Nelsen R. B.: An Introduction to Copulas. Lecture Notes in Statistics 139, Springer, New York 1999. Second edition. Springer Series in Statistics, Springer, New York 2006 · Zbl 0909.62052
[9] Nelsen R. B.: Extremes of nonexchangeability. Stat. Papers 48 (2007), 329-336 · Zbl 1110.62071 · doi:10.1007/s00362-006-0336-5
[10] Nelsen R. B., Fredricks G. A.: Diagonal copulas. Distributions with given Marginals and Moment Problems (V. Beneš and J. Štěpán, Kluwer Academic Publishers, Dordrecht 1977, pp. 121-127 · Zbl 0906.60021
[11] Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A., Úbeda-Flores M.: On the construction of copulas and quasi-copulas with given diagonal sections. Insurance Math. Econom., in press · Zbl 1152.60311 · doi:10.1016/j.insmatheco.2006.11.011
[12] Sklar A.: Fonctions de répartition á \(n\) dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231 · Zbl 0100.14202
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.