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Keywords:
copulas; diagonal section; probability mass distribution; tail dependence
copulas; diagonal section; probability mass distribution; tail dependence
Summary:
We describe a class of bivariate copulas having a fixed diagonal section. The obtained class contains both the Fréchet upper and lower bounds and it allows to describe non-trivial tail dependence coefficients along both the diagonals of the unit square.
References:
[1] Baets, B. De, Meyer, H. De, Mesiar, R.: Asymmetric semilinear copulas. Kybernetika 43 (2007), 221–233. MR 2343397 | Zbl 1136.62350
[2] Baets, B. De, Meyer, H. De, Úbeda-Flores, M.: Opposite diagonal sections of quasi-copulas and copulas. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 17 (2009), 481–490. DOI 10.1142/S0218488509006108 | MR 2591399 | Zbl 1183.62087
[3] Baets, B. De, Meyer, H. De, Úbeda-Flores, M.: Constructing copulas with given diagonal and opposite diagonal sections. Comm. Statist. Theory Methods 40 (2011), 828–843. DOI 10.1080/03610920903480866 | MR 2762928 | Zbl 1215.62051
[4] Durante, F., Fernández-Sánchez, J.: On the classes of copulas and quasi-copulas with a given diagonal section. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 19 (2011), 1–10. DOI 10.1142/S0218488511006848 | MR 2769557 | Zbl 1220.62057
[5] Durante, F., Jaworski, P.: A new characterization of bivariate copulas: Comm. Statist. Theory Methods 39 (2010), 2901–2912. DOI 10.1080/03610920903151459 | MR 2755533
[6] Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Copulas with given diagonal sections: novel constructions and applications. Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 15 (2007), 397–410. DOI 10.1142/S0218488507004753 | MR 2362234 | Zbl 1158.62324
[7] Durante, F., Kolesárová, A., Mesiar, R., Sempi, C.: Semilinear copulas. Fuzzy Sets and Systems 159 (2008), 63–76. MR 2371303
[8] Durante, F., Rodríguez-Lallena, J.A., Úbeda-Flores, M.: New constructions of diagonal patchwork copulas. Inform. Sci. 179 (2009), 3383–3391. DOI 10.1016/j.ins.2009.06.007 | MR 2574347 | Zbl 1190.62101
[9] Jaworski, P., Durante, F., Härdle, W., Rychlik, T.: Copula Theory and its Applications. Lecture Notes in Statist. - Proceedings 198. Springer, Berlin 2010. Zbl 1194.62077
[10] Joe, H.: Multivariate Models and Dependence Concepts. Monographs Statist. Appl. Probab. 73. Chapman &Hall, London 1997. MR 1462613 | Zbl 0990.62517
[11] Jwaid, T., Baets, B. De: Double-conic copulas. In: Proc. FSTA 2010 (E. P. Klement et al., eds.), 2010, p. 73.
[12] Jwaid, T., Baets, B. De, Meyer, H. De: Orbital semilinear copulas. Kybernetika 45 (2009), 1012–1029. MR 2650080 | Zbl 1186.62067
[13] Jwaid, T., Baets, B. De, Meyer, H. De: Biconic aggregation functions. Inform. Sci., in press, 2011. MR 2869868 | Zbl 1254.68256
[14] Jwaid, T., Baets, B. De, Meyer, H. De: Biconic aggregation functions with a given diagonal and opposite diagonal section. In: Proc. 7th EUSFLAT Conference. In press, 2011. MR 2869868
[15] Jwaid, T., Baets, B. De, Kalická, J., Mesiar, R.: Conic aggregation functions. Fuzzy Sets and Systems 167 (2011), 3–20. MR 2765243 | Zbl 1214.68399
[16] Klement, E. P., Kolesárová, A.: Intervals of 1-Lipschitz aggregation operators, quasi-copulas, and copulas with given affine section. Monatsh. Math. 152 (2007), 151–167. DOI 10.1007/s00605-007-0460-x | MR 2346431 | Zbl 1138.60016
[17] Klement, E. P., rová, A. Kolesá, Mesiar, R., Sempi, C.: Copulas constructed from horizontal sections. Comm. Statist. Theory Methods 36 (2007), 2901–2911. DOI 10.1080/03610920701386976 | MR 2398066
[18] Mai, J.-F.: Extendibility of Marshall–Olkin Distributions via Lévy Subordinators and an Application to Portfolio Credit Risk. PhD. Thesis, Technical University of Munich 2010.
[19] Mayor, G., Mesiar, R., Torrens, J.: On quasi-homogeneous copulas. Kybernetika 44 (2008), 745–756. MR 2488902 | Zbl 1196.62058
[20] Mesiar, R., Sarkoci, P.: Open problems posed at the Tenth International Conference on Fuzzy Set Theory and Applications (FSTA 2010, Liptovský Ján, Slovakia). Kybernetika 46 (2010), 585–599. MR 2722089 | Zbl 1211.03077
[21] Nelsen, R. B.: An Introduction to Copulas. Springer Series in Statistics. Second edition. Springer, New York 2006. MR 2197664 | Zbl 1152.62030
[22] 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. 42 (2008), 473–483. DOI 10.1016/j.insmatheco.2006.11.011 | MR 2404309 | Zbl 1152.60311
[23] Quesada-Molina, J. J., Saminger-Platz, S., Sempi, C.: Quasi-copulas with a given sub-diagonal section. Nonlinear Anal. 69 (2008), 4654–4673. DOI 10.1016/j.na.2007.11.021 | MR 2467261 | Zbl 1151.62044
[24] Rodríguez-Lallena., J. A.: A class of copulas with piecewise linear horizontal sections. J. Statist. Plan. Infer. 139 (2009), 3908–3920. DOI 10.1016/j.jspi.2009.05.032 | MR 2553777 | Zbl 1169.62045
[25] Úbeda-Flores, M.: Multivariate copulas with cubic sections in one variable. J. Nonparametr. Statist. 20 (2008), 91–98. DOI 10.1080/10485250801908355 | MR 2396278
[26] Yeh, J.: Lectures on Real Analysis. World Scientific Publishing Co. Inc., River Edge, NJ, 2000. MR 1779377 | Zbl 1039.28001
[27] Zhang, M.-H.: Modelling total tail dependence along diagonals. Insurance Math. Econom. 42 (2008), 73–80. DOI 10.1016/j.insmatheco.2007.01.002 | MR 2392071 | Zbl 1142.62097
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