Geodesic
Copulas with given values on a horizontal and a vertical section
Kybernetika, Tome 43 (2007) no. 2, pp. 209-220 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 60E05, 62H05
Keywords: copula; horizontal section; vertical section; binary aggregation operator 
@article{KYB_2007_43_2_a7,
     author = {Durante, Fabrizio and Koles\'arov\'a, Anna and Mesiar, Radko and Sempi, Carlo},
     title = {Copulas with given values on a horizontal and a vertical section},
     journal = {Kybernetika},
     pages = {209--220},
     year = {2007},
     volume = {43},
     number = {2},
     mrnumber = {2343396},
     zbl = {1140.62322},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2007_43_2_a7/}
}
TY  - JOUR
AU  - Durante, Fabrizio
AU  - Kolesárová, Anna
AU  - Mesiar, Radko
AU  - Sempi, Carlo
TI  - Copulas with given values on a horizontal and a vertical section
JO  - Kybernetika
PY  - 2007
SP  - 209
EP  - 220
VL  - 43
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_2007_43_2_a7/
LA  - en
ID  - KYB_2007_43_2_a7
ER  - 
%0 Journal Article
%A Durante, Fabrizio
%A Kolesárová, Anna
%A Mesiar, Radko
%A Sempi, Carlo
%T Copulas with given values on a horizontal and a vertical section
%J Kybernetika
%D 2007
%P 209-220
%V 43
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_2007_43_2_a7/
%G en
%F KYB_2007_43_2_a7
Durante, Fabrizio; Kolesárová, Anna; Mesiar, Radko; Sempi, Carlo. Copulas with given values on a horizontal and a vertical section. Kybernetika, Tome 43 (2007) no. 2, pp. 209-220. http://geodesic.mathdoc.fr/item/KYB_2007_43_2_a7/

[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 | MR | Zbl

[2] Carley H.: Maximum and minimum extensions of finite subcopulas. Comm. Statist. Theory Methods 31 (2002), 2151–2166 | MR | Zbl

[3] Cherubini U., Luciano, E., Vecchiato W.: Copula Methods in Finance. Wiley, New York 2004 | MR | Zbl

[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 | MR | Zbl

[6] Durante F., Sempi C.: Copula and semicopula transforms. Internat. J. Math. Sci. 2005 (2005), 645–655 | MR | Zbl

[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 | MR | Zbl

[8] Fodor J. C., Roubens M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht 1994 | Zbl

[9] Frees E. W., Valdez E. A.: Understanding relationships using copulas. North Amer. Act. J. 2 (1998), 1–25 | MR | Zbl

[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 | MR | Zbl

[12] Klement E. P., Kolesárová A.: Extensions to copulas and quasi-copulas as special 1-Lipschitz aggregation operators. Kybernetika 41 (2005), 329–348 | MR

[13] Klement E. P., Kolesárová A., Mesiar, R., Sempi C.: Copulas constructed from the horizontal section. Comm. Statist. Theory Methods, to appear | MR

[14] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 | MR | Zbl

[15] Klement E. P., Mesiar, R., Pap E.: Transformations of copulas. Kybernetika 41 (2005), 425–434 | MR

[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 | MR | Zbl

[18] Mesiar R., Szolgay J.: W-ordinals sum of copulas and quasi-copulas. In: 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 | MR | Zbl

[20] Nelsen R. B.: An Introduction to Copulas. Springer, New York 2006 | MR | Zbl

[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

[22] Nguyen H. T., Walker E. A.: A First Course in Fuzzy Logic. Chapman & Hall/CRC, Boca Raton 2006 | MR | Zbl

[23] Quesada-Molina J. J., Rodríguez-Lallena J. A.: Bivariate copulas with quadratic sections. J. Nonparametr. Statist. 5 (1995), 323–337 | MR | Zbl

[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 | MR | Zbl

[26] Sklar A.: Fonctions de répartition à $n$ dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231 | MR

[27] Sklar A.: Random variables, joint distribution functions, and copulas. Kybernetika 9 (1973), 449–460 | MR | Zbl