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...

Credit risk is one of the main risks financial institutions are exposed to. Within the last two decades, simulation-based credit portfolio models became extremely popular and replaced closed-form analytical ones as computers became more powerful. However, especially for non-homogenous and...

We introduce a new skewed and leptokurtic distribution derived from the hyperbolic secant distribution and Johnson's S transformation. Properties of this new distribution are given. Finally, we empirically demonstrate in the context of financial return data that its exibility is comparable to...

Measuring interdependence between probabilities of default (PDs) in different industry sectors of an economy plays a crucial role in financial stress testing. Thereby, regression approaches may be employed to model the impact of stressed industry sectors as covariates on other response sectors....

In this paper, we demonstrate the superiority of vine copulas over conventional copulas when modeling the dependence structure of a credit portfolio. We show statistical and economic implications of replacing conventional copulas by vine copulas for a subportfolio of the Euro Stoxx 50 and the...

Li, Fang & Tian (1994) assert that special quasi-linear means should be preferred to the simple arithmetic mean for robustness properties. The strategy that is used to show robustness is completely detached from the concepts wellknown from the theory of robust statistics. Robustness of...

J.M. Keynes (1911) shows how distributions look like for which the arithmetic, the geometric and the harmonic mean are most probable values. We propose a general class of distributions for which the quasi-arithmetic means are ML-estimators such that these distributions can be transformed into an...

Keynes (1911) derived general forms of probability density functions for which the "most probable value" is given by the arithmetic mean, the geometric mean, the harmonic mean, or the median. His approach was based on indirect (i.e., posterior) distributions and used a constant prior...

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...