Two major generalizations of the hyperbolic secant distributionhave been proposed in the statistical literature which both introduce an additionalparameter that governs the kurtosis of the generalized distribution. Thegeneralized hyperbolic secant (GHS) distribution was introduced by Harknessand...

Leptokurtic distributions can be generated by applying certainnon-linear transformations to a standard normal random variable. Withinthis work we derive general conditions for these transformations which guaranteethat the generated distributions are ordered with respect to the partialordering of...

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

The H−family of distributions or H−distributions, introduced byTukey (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...

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 parameters g and h. Therefore, the family was called family gh-distributions. We modify...

Generalized autoregressive conditional heteroskedasticity (GARCH) processes have become very popular as models for financial return data because they are able to capture volatility clustering as well as leptokurtic unconditional distributions which result from the assumption of conditionally...

Information-theoretic approaches still play a minor role in financial market analysis. Nonetheless, there have been two very similar approaches evolving during the last years, one in so-called econophysics and the other in econometrics. Both generalize the notion of GARCH processes in an...