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...

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...

In this paper we focus on symmetric generalized Fairlie-Gumbel-Morgenstern (or symmetric Sarmanov) copulas which are characterized by means of so-called generator functions. In particular, we introduce a class of generator functions which is based on univariate distributions with certain...

There is no package in R to plot bivariate distributions for discrete variables or variables given by classes. Therefore, with the help of the already implemented R routine persp R functions will be proposed for 3-D plots of the bivariate distribution of discrete variables, the so-called...

Leptokurtic distributions can be generated by applying certain non-linear transformations to a standard normal random variable. Within this work we derive general conditions for these transformations which guarantee that the generated distributions are ordered with respect to the partial...

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...