Journal of Probability and Statistics
Volume 2009 (2009), Article ID 895742, 15 pages
Research Article

On Concordance Measures for Discrete Data and Dependence Properties of Poisson Model

1Department of Economics, McGill University, Leacock Building, 855 Sherbrooke Street West, C.P. 6128, succursale Centre-ville Montreal, QC, H3A 2T7, Canada
2Département de Mathématiques et d'Informatique, Universitédu Québec à Trois-Rivières, Pavillon Ringuet, local 3060, C.P. 500, Trois-Rivières, QC, G9A 5H7, Canada
3ARC Epidemiology Unit, The University of Manchester, Oxford Road, Manchester M13 9PT, UK

Received 2 April 2009; Revised 10 November 2009; Accepted 15 December 2009

Academic Editor: Chunsheng Ma

Copyright © 2009 Taoufik Bouezmarni et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study Kendall's tau and Spearman's rho concordance measures for discrete variables. We mainly provide their best bounds using positive dependence properties. These bounds are difficult to write down explicitly in general. Here, we give the explicit formula of the best bounds in a particular Fréchet space in order to understand the behavior of the ranges of these measures. Also, based on the empirical copula which is viewed as a discrete distribution, we propose a new estimator of the copula function. Finally, we give useful dependence properties of the bivariate Poisson distribution and show the relationship between parameters of the Poisson distribution and both tau and rho.