Copulas with given values on a horizontal and a vertical section. (English) Zbl 1140.62322

Summary: 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.


62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory


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[1] Calvo T., Kolesárová A., Komorníková, M., Mesiar R.: Aggregation operators: Properties, classes and construction methods. Aggregation Operators (T. Calvo, G. Mayor, and R. Mesiar, Physica-Verlag, Heidelberg 2002, pp. 3-107 · Zbl 1039.03015
[2] Carley H.: Maximum and minimum extensions of finite subcopulas. Comm. Statist. Theory Methods 31 (2002), 2151-2166 · Zbl 1075.62558
[3] Cherubini U., Luciano, E., Vecchiato W.: Copula Methods in Finance. Wiley, New York 2004 · Zbl 1163.62081
[4] Baets B. De, Meyer H. De: Orthogonal grid construction for copulas. IEEE Trans. Fuzzy Systems (2007), to appear
[5] Durante F., Mesiar R., Papini P. L., Sempi C.: 2-increasing binary aggregation operators. Inform. Sci. 177 (2007), 111-129 · Zbl 1142.68541
[6] Durante F., Sempi C.: Copula and semicopula transforms. Internat. J. Math. Sci. 2005 (2005), 645-655 · Zbl 1078.62055
[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
[8] Fodor J. C., Roubens M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht 1994 · Zbl 0827.90002
[9] Frees E. W., Valdez E. A.: Understanding relationships using copulas. North Amer. Act. J. 2 (1998), 1-25 · Zbl 1081.62564
[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
[11] Joe H.: Multivariate Models and Dependence Concepts. Chapman & Hall, London 1997 · Zbl 0990.62517
[12] 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
[13] Klement E. P., Kolesárová A., Mesiar, R., Sempi C.: Copulas constructed from the horizontal section. Comm. Statist. Theory Methods, to appear · Zbl 1130.60017
[14] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 · Zbl 1087.20041
[15] Klement E. P., Mesiar, R., Pap E.: Transformations of copulas. Kybernetika 41 (2005), 425-434 · Zbl 1243.62019
[16] Kolesárová A., Mesiar R., Mordelová, J., Sempi C.: Discrete copulas. IEEE Trans. Fuzzy Systems 14 (2006), 698-705
[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
[18] Mesiar R., Szolgay J.: W-ordinals sum of copulas and quasi-copulas. Proc. MAGIA 2004 Conference, Kočovce 2004, pp. 78-83
[19] Morillas P. M.: A method to obtain new copulas from a given one. Metrika 61 (2005), 169-184 · Zbl 1079.62056
[20] Nelsen R. B.: An Introduction to Copulas. Springer, New York 2006 · Zbl 1152.62030
[21] Nelsen R. B., Quesada-Molina J. J., Rodríguez-Lallena J. A.: Bivariate copulas with cubic sections. J. Nonparametr. Statist. 7 (1997), 205-220 · Zbl 0898.62074
[22] Nguyen H. T., Walker E. A.: A First Course in Fuzzy Logic. Chapman & Hall/CRC, Boca Raton 2006 · Zbl 1083.03031
[23] Quesada-Molina J. J., Rodríguez-Lallena J. A.: Bivariate copulas with quadratic sections. J. Nonparametr. Statist. 5 (1995), 323-337 · Zbl 0857.62060
[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
[25] Schweizer B., Sklar A.: Probabilistic Metric Spaces. Elsevier, New York 1983 · Zbl 0546.60010
[26] Sklar A.: Fonctions de répartition à \(n\) dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231 · Zbl 0100.14202
[27] Sklar A.: Random variables, joint distribution functions, and copulas. Kybernetika 9 (1973), 449-460 · Zbl 0292.60036
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