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Title: Copulas with given values on a horizontal and a vertical section (English)
Author: Durante, Fabrizio
Author: Kolesárová, Anna
Author: Mesiar, Radko
Author: Sempi, Carlo
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 43
Issue: 2
Year: 2007
Pages: 209-220
Summary lang: English
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Category: math
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Summary: In this paper we study the set of copulas for which both a horizontal section and a vertical section have been given. We give a general construction for copulas of this type and we provide the lower and upper copulas with these sections. Symmetric copulas with given horizontal section are also discussed, as well as copulas defined on a grid of the unit square. Several examples are presented. (English)
Keyword: copula
Keyword: horizontal section
Keyword: vertical section
Keyword: binary aggregation operator
MSC: 60E05
MSC: 62H05
idZBL: Zbl 1140.62322
idMR: MR2343396
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Date available: 2009-09-24T20:22:58Z
Last updated: 2012-06-06
Stable URL: http://hdl.handle.net/10338.dmlcz/135767
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Reference: [1] Calvo T., Kolesárová A., Komorníková, M., Mesiar R.: Aggregation operators: Properties, classes and construction methods.In: Aggregation Operators (T. Calvo, G. Mayor, and R. Mesiar, eds.), Physica–Verlag, Heidelberg 2002, pp. 3–107 Zbl 1039.03015, MR 1936383
Reference: [2] Carley H.: Maximum and minimum extensions of finite subcopulas.Comm. Statist. Theory Methods 31 (2002), 2151–2166 Zbl 1075.62558, MR 1945852
Reference: [3] Cherubini U., Luciano, E., Vecchiato W.: Copula Methods in Finance.Wiley, New York 2004 Zbl 1163.62081, MR 2250804
Reference: [4] Baets B. De, Meyer H. De: Orthogonal grid construction for copulas.IEEE Trans. Fuzzy Systems (2007), to appear
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
Reference: [6] Durante F., Sempi C.: Copula and semicopula transforms.Internat. J. Math. Sci. 2005 (2005), 645–655 Zbl 1078.62055, MR 2172400
Reference: [7] Erdely A., González-Barrios J. M.: On the construction of families of absolutely continuous copulas with given restrictions.Comm. Statist. Theory Methods 35 (2006), 649–659 Zbl 1098.60017, MR 2282880
Reference: [8] Fodor J. C., Roubens M.: Fuzzy Preference Modelling and Multicriteria Decision Support.Kluwer Academic Publishers, Dordrecht 1994 Zbl 0827.90002
Reference: [9] Frees E. W., Valdez E. A.: Understanding relationships using copulas.North Amer. Act. J. 2 (1998), 1–25 Zbl 1081.62564, MR 1988432
Reference: [10] Genest C., Favre A.-C.: Everything you always wanted to know about copula modeling but were afraid to ask.J. Hydrologic Engrg. 12 (2007), to appear
Reference: [11] Joe H.: Multivariate Models and Dependence Concepts.Chapman & Hall, London 1997 Zbl 0990.62517, MR 1462613
Reference: [12] Klement E. P., Kolesárová A.: Extensions to copulas and quasi-copulas as special 1-Lipschitz aggregation operators.Kybernetika 41 (2005), 329–348 MR 2181422
Reference: [13] Klement E. P., Kolesárová A., Mesiar, R., Sempi C.: Copulas constructed from the horizontal section.Comm. Statist. Theory Methods, to appear MR 2398066
Reference: [14] Klement E. P., Mesiar, R., Pap E.: Triangular Norms.Kluwer Academic Publishers, Dordrecht 2000 Zbl 1087.20041, MR 1790096
Reference: [15] Klement E. P., Mesiar, R., Pap E.: Transformations of copulas.Kybernetika 41 (2005), 425–434 MR 2180355
Reference: [16] Kolesárová A., Mesiar R., Mordelová, J., Sempi C.: Discrete copulas.IEEE Trans. Fuzzy Systems 14 (2006), 698–705
Reference: [17] McNeil A. J., Frey, R., Embrechts P.: Quantitative Risk Management.Concepts, Techniques and Tools. Princeton University Press, Princeton, N.J. 2005 Zbl 1089.91037, MR 2175089
Reference: [18] Mesiar R., Szolgay J.: W-ordinals sum of copulas and quasi-copulas.In: Proc. MAGIA 2004 Conference, Kočovce 2004, pp. 78–83
Reference: [19] Morillas P. M.: A method to obtain new copulas from a given one.Metrika 61 (2005), 169–184 Zbl 1079.62056, MR 2159414
Reference: [20] Nelsen R. B.: An Introduction to Copulas.Springer, New York 2006 Zbl 1152.62030, MR 2197664
Reference: [21] Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A.: Bivariate copulas with cubic sections.J. Nonparametr. Statist. 7 (1997), 205–220 MR 1443354
Reference: [22] Nguyen H. T., Walker E. A.: A First Course in Fuzzy Logic.Chapman & Hall/CRC, Boca Raton 2006 Zbl 1083.03031, MR 2180829
Reference: [23] Quesada-Molina J. J., Rodríguez-Lallena J. A.: Bivariate copulas with quadratic sections.J. Nonparametr. Statist. 5 (1995), 323–337 Zbl 0857.62060, MR 1379534
Reference: [24] Salvadori G., Michele C. De, Kottegoda N. T., Rosso R.: Extremes in Nature.An Approach Using Copulas. (WTS Library Series, Vol. 56.) Springer–Verlag, Berlin 2007
Reference: [25] Schweizer B., Sklar A.: Probabilistic Metric Spaces.Elsevier, New York 1983 Zbl 0546.60010, MR 0790314
Reference: [26] Sklar A.: Fonctions de répartition à $n$ dimensions et leurs marges.Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 MR 0125600
Reference: [27] Sklar A.: Random variables, joint distribution functions, and copulas.Kybernetika 9 (1973), 449–460 Zbl 0292.60036, MR 0345164
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