Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 38/2001
Characterizations of measures of concordance depend on an ordering of bivariate distributions with fixed marginals or use the concept of a copula to define a ordering without fixed but with continuous marginals. Ordinal variables with a fixed number of categories have discrete bivariate distributions. But for discrete distributions copulas are not unique. Therefore, Scarsini (1984) propose an ordering for discrete distributions. But it is not possible to check whether a measure of concordance hold this ordering. Following Scarsini we consider for discrete distributions a special copula and define an ordering based on this special copula. We give formulas for the traditional measures of concordance (like Kendall's Pi and Spearman's p) which hold the ordering and are only slight modifications of the well-known formulas.