Previous |  Up |  Next


Title: Univariate conditioning of copulas (English)
Author: Mesiar, Radko
Author: Jágr, Vladimír
Author: Juráňová , Monika
Author: Komorníková, Magda
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 44
Issue: 6
Year: 2008
Pages: 807-816
Summary lang: English
Category: math
Summary: The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archimedean copulas. Several interesting examples are given. Especially, any Ali-Mikhail-Haq copula with a given parameter λ > 0 allows to construct via conditioning any Ali-Mikhail-Haq copula with parameter μ $\in $ [0,λ]. (English)
Keyword: conditioning
Keyword: gluing
Keyword: g-ordinal sum
Keyword: construction of copulas
MSC: 60E05
MSC: 62H05
idZBL: Zbl 1196.62059
idMR: MR2488908
Date available: 2009-09-24T20:40:26Z
Last updated: 2013-09-21
Stable URL:
Reference: [1] Javid A. Ahmadi: Copulas with truncation-invariance property.Comm. Statist. A – Theory Methods, to appear MR 2589808
Reference: [2] Calvo T., Kolesárová A., Komorníková, M., Mesiar R.: Aggregation Operators: Properties, Classes and Construction Methods.(Studies in Fuzziness and Soft Computing – Aggregation Operators, New Trend and Applications.) Physica-Verlag, Heidelberg 2002, pp. 3–106 Zbl 1039.03015, MR 1936383
Reference: [3] Charpentier A., Juri A.: Limiting dependence structures for tail events, with applications to credit derivatives.J. Appl. Probab. 43 (2006), 563–586 Zbl 1117.62049, MR 2248584, 10.1239/jap/1152413742
Reference: [4] Durante F., Foschi, B., Spizzichino S.: Threshold copulas and positive dependence.Statist. Probab. Lett., to appear Zbl 1148.62032, MR 2474379
Reference: [5] Durante F., Mesiar R., Papini P. L., Sempi C.: 2-Increasing binary aggregation operators.Inform. Sci. 177 (2007), 111–129 Zbl 1142.68541, MR 2272737, 10.1016/j.ins.2006.04.006
Reference: [6] Durante F., Saminger-Platz, S., Sarkoci P.: On representations of 2-increasing binary aggregation functions.Inform. Sci. 178 (2008), 4534–4541 Zbl 1163.68340, MR 2467125, 10.1016/j.ins.2008.08.004
Reference: [7] Durante F., Saminger-Platz, S., Sarkoci P.: Rectangular patchwork for bivariate copulas and tail dependence.Comm. Statist. A – Theory Methods, to appear Zbl 1170.62329, MR 2596930
Reference: [8] Juri A., Wüthrich M. V.: Copula convergence theorems for tail events.Insurance Math. Econom. 30 (2002), 405–420 Zbl 1039.62043, MR 1921115, 10.1016/S0167-6687(02)00121-X
Reference: [9] Juri A., Wüthrich M. V.: Tail dependence from a distributional point of view.Extreme 6 (2003), 213–246 Zbl 1049.62055, MR 2081852, 10.1023/B:EXTR.0000031180.93684.85
Reference: [10] Klement E. P., Mesiar, R., Pap E.: Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms.Fuzzy Sets and Systems 104 (1999), 3–14 Zbl 0953.26008, MR 1685803
Reference: [11] Mesiar R., Szolgay J.: $W$-ordinal sums of copulas and quasi-copulas.In: Proc. MAGIA 2004 Conference, Kočovce 2004, pp. 78–83
Reference: [12] Nelsen R. B.: An Introduction to Copulas.Second edition. Springer, Berlin 2006 Zbl 1152.62030, MR 2197664
Reference: [13] Siburg K. F., Stoimenov P. A.: Gluing copulas.Comm. Statist. A – Theory Methods 37 (2008), 3124–3134 MR 2467756, 10.1080/03610920802074844
Reference: [14] Sklar M.: Fonctions de répartition à $n$ dimensions et leurs marges.Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 MR 0125600


Files Size Format View
Kybernetika_44-2008-6_6.pdf 816.4Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo