Skip to content
BY 4.0 license Open Access Published by De Gruyter Open Access December 16, 2020

Multivariate medial correlation with applications

  • Helena Ferreira EMAIL logo and Marta Ferreira
From the journal Dependence Modeling


We define a multivariate medial correlation coefficient that extends the probabilistic interpretation and properties of Blomqvist’s β coefficient, incorporates multivariate marginal dependencies and it preserves a partial ordering stronger than concordance relation. We illustrate the results in some models and provide an application on real datasets.

MSC 2010: 62H20


[1] Blomqvist, N. (1950). On a measure of dependence between two random variables. Ann. Math. Statist. 21(4), 593–600.10.1214/aoms/1177729754Search in Google Scholar

[2] Cortez, P., A. Cerdeira, F. Almeida, T. Matos and J.Reis (2009). Modeling wine preferences by data mining from physicochemical properties. Decis. Support Syst. 47(4), 547–553.10.1016/j.dss.2009.05.016Search in Google Scholar

[3] Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman and Hall, London.Search in Google Scholar

[4] Joe, H. (1990). Multivariate Concordance. J. Multivariate Anal. 35(1), 12–30.10.1016/0047-259X(90)90013-8Search in Google Scholar

[5] Joe, H. (2015). Dependence Modeling with Copulas. CRC Press, Boca Raton FL.Search in Google Scholar

[6] Lebedev, A.V. (2019). On the Interrelation between dependence coefficients of bivariate extreme value copulas. Markov Process. Relat. 25(4), 639–648.Search in Google Scholar

[7] Nelsen, R.B. (2002). Concordance and Copulas: A Survey. In C.M. Cuadras, Fortiana J., Rodriguez-Lallena J.A. (Eds.) Distributions With Given Marginals and Statistical Modelling, pp 169–177. Springer, Dordrecht.10.1007/978-94-017-0061-0_18Search in Google Scholar

[8] Nelsen, R.B. (2006). An Introduction to Copulas. Second edition. Springer, New York.Search in Google Scholar

[9] Scarsini, M. (1984). On Measures of Concordance. Stochastica 8(3), 201–218.Search in Google Scholar

[10] Schmid, F. and R. Schmidt (2007). Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence. Metrika 66(3), 323–354.10.1007/s00184-006-0114-3Search in Google Scholar

[11] Taylor, M. D. (2007). Multivariate measures of concordance. Ann. Inst. Statist. Math. 59(4), 789–806.10.1007/s10463-006-0076-2Search in Google Scholar

[12] Taylor, M. D. (2016). Multivariate measures of concordance for copulas and their marginals. Depend. Model. 4, 224–23610.1515/demo-2016-0013Search in Google Scholar

[13] Úbeda-Flores, M. (2005) Multivariate versions of Blomqvist’s beta and Spearman’s footrule. Ann. Inst. Statist. Math. 57(4), 781–788.10.1007/BF02915438Search in Google Scholar

Received: 2020-09-28
Accepted: 2020-11-23
Published Online: 2020-12-16

© 2020 Helena Ferreira et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Downloaded on 24.3.2023 from
Scroll Up Arrow