Abstract
Abstract In this paper we survey relationships between concordance of random variables and their copulas. We focus on the relationship between concordance and measures of association such as Kendall’s tau, Spearman’s rho and Gini’s coefficient. Extensions to the multivariate case are also discussed.
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References
Bertino, S. (1977), Sulla dissomiglianza tra mutabili cicliche. Metron 35, 53–88.
Blomqvist, N. (1950), On a measure of dependence between two random variables. Annals of Mathematical Statistics 21, 593–600.
Cuadras, C. M. and J. Augé (1981), A continuous general multivariate distribution and its properties. Communications in Statistics -Theory Methods A10, 339–353.
Frank, M. J. (1979), On the simultaneous associativity of F(x, y) and x + y-F(x, y). Aequationes Mathematicae 19, 194–226.
Genest, C. and J. MacKay (1986a), Copulas archimédiennes et familles de lois bidimensionnelles dont les marges sont données. Canadian Journal of Statistics 14, 145–159.
Genest, C. and J. MacKay (1986b), The joy of copulas: Bivariate distributions with uniform marginals. American Statistician 40, 280–285.
Hoeffding, W. (1940), Masstabinvariante Korrelationstheorie. Schriften des Matematischen Instituts und des Instituts für Angewandte Mathematik der Universität Berlin 5, Heft 3, 179–233.
Hoeffding, W. (1947), On the distribution of the rank correlation coefficient t when the variates are not independent. Biometrika 34, 183–196.
Joe, H. (1990), Multivariate concordance. Journal of Multivariate Analysis 35, 12–30.
Kimeldorf, G. and A. Sampson (1987), Positive dependence orderings. Annals of the Institute of Statistical Mathematics 39, 113–128.
Kimeldorf, G. and A. Sampson (1989), A framework for positive dependence. Annals of the Institute of Statistical Mathematics 41, 31–45.
Kruskal, W. H. (1958), Ordinal measures of association. Journal of the American Statistical Association 53, 814–861.
Li, X., Mikusiński, and M. D. Taylor (2001), Some integration-by-parts formulas involving 2copulas.
Marshall, A. W. and I. Olkin (1967), A multivariate exponential distribution. Journal of the American Statistical Association 62, 30–44.
Nelsen, R. B. (1996), Nonparametric measures of multivariate association. In L. Rüschendorf, B. Schweizer, and M. D. Taylor, (eds.): Distributions with Fixed Marginals and Related Topics, Institute of Mathematical Statistics, Hayward, CA, pp. 223–232.
Nelsen, R. B. (1998), Concordance and Gini’s measure of association. Nonparametric Statistics 9, 227–238.
Nelsen, R. B. (1999), An Introduction to Copulas. New York: Springer.
Scarsini, M. (1984), On measures of concordance. Stochastica 8, 201–218.
Schweizer, B. and E. F. Wolff (1981), On nonparametric measures of dependence for random variables. Annals of Statistics 9, 870–885.
Sklar, A. (1959), Fonctions de répartition á n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229–231.
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Nelsen, R.B. (2002). Concordance and Copulas: A Survey. In: Cuadras, C.M., Fortiana, J., Rodriguez-Lallena, J.A. (eds) Distributions With Given Marginals and Statistical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0061-0_18
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DOI: https://doi.org/10.1007/978-94-017-0061-0_18
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