The shape of a probability distribution is often summarized by the distribution's skewness and kurtosis. Starting from a symmetric "parent" density f on the real line, we can modify its shape (i.e. introduce skewness and in-/decrease kurtosis) if f is appropriately weighted. In particular, every...

Constructing skew and heavy-tailed distributions by transforming a standard normal variable goes back to Tukey (1977) and was extended and formalized by Hoaglin (1983) and Martinez & Iglewicz (1984). Applications of Tukey's GH distribution family - which are composed by a skewness transformation...

One possibility to construct heavy tail distributions is to directly manipulate a standard Gaussian random variable by means of transformations which satisfy certain conditions. This approach dates back to Tukey (1960) who introduces the popular H-transformation. Alternatively, the...

A new test for constant correlation is proposed. The TC-test is derived as Lagrange multiplier (LM) test. Whereas most of the traditional tests (e.g. Jennrich, 1970, Tang, 1995 and Goetzmann, Li & Rouwenhorst, 2005) specify the unknown correlations as piecewise constant, our model-setup for the...

Leptokurtic or platykurtic distributions can, for example, be generated by applying certain non-linear transformations to a Gaussian random variable. Within this work we focus on the class of so-called power transformations which are determined by their generator function. Examples are the...

We present a non-parametric tail dependence estimator which arises naturally from a specific regression model. Above that, this tail dependence estimator also results from a specific copula mixture. -- Upper tail dependence ; nonparametric estimation ; copula

We present a new family of copulas ("generalized mean copulas") which is positive comprehensive and allows for upper tail dependence. It includes the Spearman copula and a specific Fréchet copula as special cases. Some properties and a generalized tail dependence estimator are derived. Finally,...

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two...

Since the pioneering work of Embrechts and co-authors in 1999, copula models enjoy steadily increasing popularity in finance. Whereas copulas are well-studied in the bivariate case, the higher-dimensional case still offers several open issues and it is by far not clear how to construct copulas...

Recently, Liebscher (2006) introduced a general construction scheme of d-variate copulas which generalizes the Archimedean family. Similarly, Morillas (2005) proposed a method to obtain a variety of new copulas from a given d-copula. Both approaches coincide only for the particular subclass of...