Quesada-Molina, J. J.; Rodríguez-Lallena, J. A. Bivariate copulas with quadratic sections. (English) Zbl 0857.62060 J. Nonparametric Stat. 5, No. 4, 323-337 (1995). Summary: We present a method for constructing bivariate copulas with quadratic sections. These copulas are derived from simple univariate real-valued functions on the interval \([0,1]\). As a consequence, various positive dependence properties (such as quadrant dependence and total positivity), measures of association (such as Spearman’s rho and Kendall’s tau), stochastic orderings, and various notions of symmetry are shown to be equivalent to certain simple properties of the above-mentioned univariate functions. Several examples, some of which can be viewed as generalizations of the Farlie-Gumbel-Morgenstern family, are presented to illustrate the facility with which these copulas can be constructed. Cited in 20 Documents MSC: 62H20 Measures of association (correlation, canonical correlation, etc.) 62H05 Characterization and structure theory for multivariate probability distributions; copulas Keywords:families of bivariate copulas; measures of dependence; concepts of dependence; radial symmetry; quadratic sections; positive dependence properties; quadrant dependence; total positivity; Spearman’s rho; Kendall’s tau; stochastic orderings; Farlie-Gumbel-Morgenstern family PDF BibTeX XML Cite \textit{J. J. Quesada-Molina} and \textit{J. A. Rodríguez-Lallena}, J. Nonparametric Stat. 5, No. 4, 323--337 (1995; Zbl 0857.62060) Full Text: DOI OpenURL References: [1] DOI: 10.2307/3315838 · Zbl 0738.62057 [2] DOI: 10.1214/aoms/1177692646 · Zbl 0263.62011 [3] DOI: 10.2307/3314660 · Zbl 0605.62049 [4] DOI: 10.2307/2684602 [5] DOI: 10.1214/aoms/1177699260 · Zbl 0146.40601 [6] Nelsen R.B., Advances in Probability Distributions with Given Marginals [7] DOI: 10.1080/10485259308832574 · Zbl 1380.62227 [8] Quesada-Molina J. J., Submitted to the Journal of the I talian Statistical Society [9] Rodriguez-Lallena, Aplicaciones (1993) [10] Schweizer B., Probabilistic Metric Spaces (1983) · Zbl 0546.60010 [11] DOI: 10.1214/aos/1176345528 · Zbl 0468.62012 [12] Sklar A., Publications de I’Institut de Statistique de l’Université de Paris 8 pp 229– (1959) [13] Sklar A., and copulas. Kybernetika 9 pp 449– (1973) [14] Wolff E.F., Measures of dependence derived from copulas (1977) 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.