Article
Full entry |
PDF
(0.8 MB)
Feedback
PDF
(0.8 MB)
Feedback
Keywords:
copula; dependence ordering; FGM family; measure of association; symmetry; transformation
copula; dependence ordering; FGM family; measure of association; symmetry; transformation
Summary:
In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.
References:
[1] M. M. Ali, N. N. Mikhail, and M. S. Haq: A class of bivariate distributions including the bivariate logistic. J. Multivariate Anal. 8 (1978), 405–412. MR 0512610
[2] E. Alvoni, P. L. Papini, and F. Spizzichino: On a class of transformations of copulas and quasi-copulas. Fuzzy Sets and Systems 50 (2009), 334–343. MR 2473107
[3] R. Baker: An-order-statistics-based method for constructing distributions with fixed marginals. J. Multivariate Anal. 99 (2008), 2312–2327. MR 2463391
[4] J. Behboodian, A. Dolati, and M. Úbeda-Flores: Measures of association based on average quadrant dependence. J. Probab. Statist. Sci. 3 (2005), 161–173.
[5] G. Beliakov, A. Pradera, and T. Calvo: Aggregation Functions: A Guide for Practitioners. Springer, New York 2007.
[6] T. Calvo, G. Mayor, and R. Mesiar (eds.): Aggregation Operators: New Trends and Applications. Physica-Verlag, Heidelberg 2002. MR 1936383
[7] C. M. Cuadras: Constructing copula functions with weighted geometric means. J. Statist. Plann. Inference 139 (2009), 3766–3772. MR 2553761
[8] B. De Baets, H. De Meyer, and S. Díaz: On an idempotent transformation of aggregation functions and its application on absolutely continuous Archimedean copulas. Fuzzy Sets and Systems 160 (2009), 733–751. MR 2493272
[9] D. Drouet Mari and S. Kotz: Correlation and Dependence. Imperial College Press, London 2001. MR 1835042
[10] F. Durante: Construction of non-exchangeable bivariate distribution functions. Statist. Papers 50 (2009), 383–391. MR 2476195
[11] F. Durante and C. Sempi: Copula and semicopula transforms. Internat. J. Math. Math. Sci. 4 (2005), 645–655. MR 2172400
[12] F. Durante, R. Mesiar, P. L. Papini, and C. Sempi: 2-increasing binary aggregation operators. Inform. Sci. 177 (2007), 111-129. MR 2272737
[13] V. Durrleman, A. Nikeghbali, and T. Roncalli: A Simple Transformation of Copulas. Technical Report. Groupe de Research Operationnelle Credit–Lyonnais 2000.
[14] P. Hájek and R. Mesiar: On copulas, quasi-copulas and fuzzy logic. Soft Computing 12 (2008), 1239–1243.
[15] H. Joe: Multivariate Models and Dependence Concepts. Chapman and Hall, London 1997. MR 1462613 | Zbl 0990.62517
[16] E. P. Klement, R. Mesiar, and E. Pap: Triangular Norms. Kluwer, Dordrecht 2000. MR 1790096
[17] E. P. Klement, R. Mesiar, and E. Pap: Archimax copulas and invariance under transformations. C.R. Acad. Sci. Paris, Ser. I 340 (2005), 755–758. MR 2141065
[18] E. P. Klement, R. Mesiar, and E. Pap: Transformations of copulas. Kybernetika 41 (2005), 425–434. MR 2180355
[19] R. Mesiar and C. Sempi: Ordinal sums and idempotents of copulas. Aequationes Math. (to appear) MR 2640277
[20] P. M. Morillas: A method to obtain new copulas from a given one. Metrika 61 (2005), 169–184. MR 2159414 | Zbl 1079.62056
[21] R. B. Nelsen: Some concepts of bivariate symmetry. J. Nonparametric Statist. 3 (1993), 95–101. MR 1272164
[22] R. B. Nelsen: An Introduction to Copulas. Second Edition. Springer, New York 2006. MR 2197664 | Zbl 1152.62030
[23] J. A. Rodríguez-Lallena and M. Úbeda-Flores: A new class of bivariate copulas. Statist. Probab. Lett. 66 (2004), 315–325. MR 2045476
[24] M. Scarsini: On measures of concordance. Stochastica 8 (1984), 201–218. MR 0796650 | Zbl 0582.62047
[25]
A. Sklar: Fonctions de répartition $\grave{\mathrm {
a}}$ n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229–231. MR 0125600
[26] A. Sklar: Random variables, joint distributions, and copulas. Kybernetika 9 (1973), 449–460. MR 0345164
Search
Partner of
