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Are copulas unimodal? (English) Zbl 1028.60009
From the introduction: It is Sklar who in 1959 coined the term copula for a distribution whose margins are uniform on the unit interval. … An important property of a distribution is unimodality. It is then natural to ask whether copulas are unimodal. Multivariate unimodality takes different forms so we choose here the most used ones (central convex, block and star unimodality) and examine copulas with respect to them.

##### MSC:
 6e+06 Probability distributions: general theory 6.2e+11 Characterization and structure theory of statistical distributions
##### Keywords:
copula; unimodality; Archimedean case; diagonal sections
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##### References:
 [1] Bertin, E.; Cuculescu, I.; Theodorescu, R., Unimodality of probability measures, (1997), Kluwer Dordrecht · Zbl 0876.60001 [2] Capéraà, P.; Fougères, A.-L.; Genest, C., Bivariate distributions with given extreme value attractor, J. multivariate anal., 72, 30-49, (2000) · Zbl 0978.62043 [3] Cuculescu, I.; Theodorescu, R., Extreme value attractors for star unimodal copulas, C.R. acad. sci. Paris Sér. I math., 334, 689-692, (2002) · Zbl 0996.60026 [4] I. Cuculescu, R. Theodorescu, Maximum domain of attraction for unimodal copulas, Investigación Oper. 2002, in print. [5] Dharmadhikari, S.W.; Joag-dev, K., Unimodality, convexity, and applications, (1988), Academic Press New York [6] Fréchet, M., Remarques sur la note précédente, C. R. acad. sci. Paris Sér. I math., 246, 2719-2721, (1958) · Zbl 0084.35804 [7] Genest, C.; Quesada Molina, J.J.; Rodrı́guez Lallena, J.A.; Sempi, C., A characterization of quasi-copulas, J. multivariate anal., 69, 193-205, (1999) · Zbl 0935.62059 [8] Nelsen, R.B., An introduction to copulas, (1999), Springer New York · Zbl 0909.62052 [9] Sklar, A., Fonctions de répartition à n dimensions et leur marges, Publ. inst. statist. univ. Paris, 8, 229-231, (1959) · Zbl 0100.14202
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