# zbMATH — the first resource for mathematics

Remarks on two product-like constructions for copulas. (English) Zbl 1136.60306
Summary: 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 product and the $$*$$-product for copulas introduced by W. F. Darsow, B. Nguyen and E. T. Olsen [Ill. J. Math. 36, No. 4, 600–642 (1992; Zbl 0770.60019)]. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.

##### MSC:
 60E05 Probability distributions: general theory 62H05 Characterization and structure theory for multivariate probability distributions; copulas
##### Keywords:
copula; ordinal sum; shuffle of Min; concordance
Full Text:
##### References:
 [1] Darsow W. F., Nguyen, B., Olsen E. T.: Copulas and Markov processes. Illinois J. Math. 36 (1992), 600-642 · Zbl 0770.60019 [2] Baets B. De, Meyer H. De: Copulas and the pairwise probabilistic comparison of ordered lists. 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 · Zbl 0990.62517 [5] Kolesárová A., Mesiar, R., Sempi C.: Three copulas and compatibility. Proc. IPMU 2006 (B. Bouchon-Meunier and R. Yager, Vol. 1, Éditions E.D.K., Paris 2006, pp. 658-663 [6] Mesiar R., Szolgay J.: W-ordinal sums of copulas and quasi-copulas. 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 · Zbl 0768.60017 · eudml:39282 [8] Nelsen R. B.: An Introduction to Copulas. Springer, New York 2006 · Zbl 1152.62030 [9] Schweizer B., Sklar A.: Probabilistic Metric Spaces. North-Holland, New York 1983. Second edition: Dover Publications, Mineola, New York 2005 · Zbl 0546.60010 [10] Sklar A.: Fonctions de répartition à $$n$$ dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 (1959), 229-231 · Zbl 0100.14202
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.