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discrete copulas; r-symmetric permutations; independence
In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.
[1] Aguiló I., Suñer, J., Torrens J.: Matrix representation of discrete quasi-copulas. Fuzzy Sets and Systems 159 (2008), 1658–1672 DOI 10.1016/j.fss.2007.10.004 | MR 2419976
[2] Alsina C., Frank, M. J, Schweizer B.: Associative Functions: Triangular Norms and Copulas. World Scientific Publishing Co., Singapore 2006 MR 2222258 | Zbl 1100.39023
[3] Deheuvels P.: La fonction de dépendance empirique et ses propriétés. Un test non paramétrique d’indépendance. Acad. Roy. Belg. Bull. Cl. Sci. 65 (1979), 5, 274–292 MR 0573609 | Zbl 0422.62037
[4] Klement E. P., Mesiar, R., Pap E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000 MR 1790096 | Zbl 1087.20041
[5] Klement E. P., Mesiar R.: Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms. Elsevier, Amsterdam 2005 MR 2166082 | Zbl 1063.03003
[6] Kolesárová A., Mesiar R., Mordelová, J., Sempi C.: Discrete copulas. IEEE Trans. Fuzzy Systems. 14 (2006), 698–705 DOI 10.1109/TFUZZ.2006.880003
[7] Kolesárová A., Mordelová J.: Quasi-copulas and copulas on a discrete scale. Soft Computing 10 (2006), 495–501 DOI 10.1007/s00500-005-0524-6 | Zbl 1096.60012
[8] Mayor G., Suñer, J., Torrens J.: Copula-like operations on finite settings. IEEE Trans. Fuzzy Systems 13 (2005), 468–477 DOI 10.1109/TFUZZ.2004.840129
[9] Mayor G., Suñer, J., Torrens J.: Sklar’s Theorem in finite settings. IEEE Trans. Fuzzy Systems 15 (2007), 410–416 DOI 10.1109/TFUZZ.2006.882462
[10] Mesiar R.: Discrete copulas – what they are. In: Joint EUSFLAT-LFA 2005, Conference Proceedings (E. Montseny and P. Sobrevilla, eds.) Universitat Politecnica de Catalunya, Barcelona 2005, pp. 927–930
[11] Miller W.: The maximum order of an element of a finite symmetric group. Amer. Math. Monthly 94 (1987), 6, 497–506 DOI 10.2307/2322839 | MR 0935414 | Zbl 1191.11027
[12] Nelsen R. B.: An Introduction to Copulas. Second edition. Springer, New York 2006 MR 2197664 | Zbl 1152.62030
[13] Schweizer B., Sklar A.: Probabilistic Metric Spaces. North-Holland, New York 1983 MR 0790314 | Zbl 0546.60010
[14] Skiena S.: The cycle structure of permutations. In: Implementing Discrete Mathematics: Combinatorial and Graph Theory with Mathematica. Addison-Wesley, Reading, MA 1990, pp. 20–24 MR 1061378
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