In almost all studies concerned with the distribution of financial data skewness and leptokurtosis will be measured by the third and the fourth standardized moments. Additionally, there is the problem of some severe outliers in the data. Therefore, skewness and leptokurtosis will be...

Idempotence is a well-known property of functionals of location. It means that the value of the functional at a singular distribution must be identically to the mass point of this distribution. First, we explain the role of idempotence in the known axiomizations of location functionals. Then we...

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...

Tukey (1960) derived via the technique of transformation of variables starting from the normal distribution a family of skewed and leptokurtic distributions. Skewness and leptokurtosis are determined by two parametersg and h. Therefore, the family was called gh-distributions. We modify Tukeys...

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...

Velleman & Wilkinson (1993) give a lot of examples to show that the hierarchy of scalers introduced by Stevens is misleading. We will show that these examples gain are misleading if we accept that most real data sets stem come derived measurement. For derived measurement the absolute scale is...