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Remarks on Two Product-like Constructions for Copulas
Kybernetika, Tome 43 (2007) no. 2, pp. 235-244
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We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the $\ast $-product and the $\star $-product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.
We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the $\ast $-product and the $\star $-product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.
Classification : 60E05, 62H05
Keywords: copula; ordinal sum; shuffle of Min; concordance 
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Durante, Fabrizio; Klement, Erich Peter; Quesada-Molina, José; Sarkoci, Peter. Remarks on Two Product-like Constructions for Copulas. Kybernetika, Tome 43 (2007) no. 2, pp. 235-244. http://geodesic.mathdoc.fr/item/KYB_2007_43_2_a9/

[1] Darsow W. F., Nguyen, B., Olsen E. T.: Copulas and Markov processes. Illinois J. Math. 36 (1992), 600–642 | MR | Zbl

[2] Baets B. De, Meyer H. De: Copulas and the pairwise probabilistic comparison of ordered lists. In: Proc. 10th International Conference IPMU, Perugia 2004, pp. 1091–1098

[3] Durante F., Klement E. P., Quesada-Molina J. J.: Copulas: compatibility and Fréchet classes. Submitted

[4] Joe H.: Multivariate Models and Dependence Concepts. Chapman & Hall, London 1997 | MR | Zbl

[5] Kolesárová A., Mesiar, R., Sempi C.: Three copulas and compatibility. In: Proc. IPMU 2006 (B. Bouchon-Meunier and R. Yager, eds.), Vol. 1, Éditions E.D.K., Paris 2006, pp. 658–663

[6] Mesiar R., Szolgay J.: W-ordinal sums of copulas and quasi-copulas. In: Proc. MAGIA 2004 Conference, Kočovce, Slovak Republic 2004, pp. 78–83

[7] Mikusiński P., Sherwood, H., Taylor M. D.: Shuffles of Min. Stochastica 13 (1992), 61–74 | MR | Zbl

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

[9] Schweizer B., Sklar A.: Probabilistic Metric Spaces. North–Holland, New York 1983. Second edition: Dover Publications, Mineola, New York 2005 | MR | Zbl

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