A generalization of the hyperbolic secant distribution which allows both for skewness and for leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to...

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...

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...

Calculating a large number of tail probabilities or tail quantiles for a given distribution families becomes very challenging, if both the cumulative and the inverse distribution function are not available in closed form. In case of the Gaussian and Student t distribution, quantile...