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...

Es ist mittlerweile weitgehend unbestritten, dass der demographische Wandel eine grundlegende Reform der gesetzlichen Rentenversicherung erforderlich macht. Dies soll im Wesentlichen durch die Einführung einer Zusatzrente auf Kapitalbasis (Teilkapitaldeckungsverfahren) erfolgen. Der Beitrag...

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...

Two major generalizations of the hyperbolic secant distribution have been proposed in the statistical literature which both introduce an additional parameter that governs the kurtosis of the generalized distribution. The generalized hyperbolic secant (GHS) distribution was introduced by Harkness...

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...

Using the Gaussian distribution as statistical model for data sets is widely spread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation...

The H-family of distributions or H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation of the standard normal distribution and allow for leptokurtosis represented by the parameter h. Alternatively, Haynes, MacGillivray and Mengersen (1997) generated...

There are several possibilities to introduce skewness into a symmetric distribution. One of these procedures applies two dfferent parameters of scale - with possibly different weights - to the positive and the negative part of a symmetric density. Within this work we show that this technique...

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...