Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 26/1998
We derive almost all known measures of skewness from differences of probability or differences of quantiles. Because ordinal variables are measured non-uniquely with respect to strictly increasing transformations functions of differences of quantiles cannot be used to describe the skewness of these variables. Therefore, we construct a class of very simple measures of skewness as functions of differences of probability. The concepts are illustrated by the binomial- and the beta-distribution.