Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/29584
Authors: 
Fischer, Matthias J.
Horn, Armin
Klein, Ingo
Year of Publication: 
2003
Series/Report no.: 
Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 52/2003
Abstract: 
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 (H-transformation) of a standard normal distribution (or, more general, of a symmetric distribution) Z and allow for leptokurtosis represented by the (elongation) parameter h > 0. In order to additionally take skewness into account by means of certain transformations, several generalizations and extensions (HQ,HH,GH,GK;...) have been proposed in the literature. Within this work we 'complete' this class of Tukey-type distributions by introducing KQ- and JQ-distributions on the one side and KK-, JJ- and e GJ-distributions on the other side. Moreover, we empirically compare the goodness-of-fit of such Tukey-type distributions for different symmetrical distributions Z (here: Gaussian, logistic and hyperbolic secant distribution) in the context of financial return data. In particular, the interplay between Z and the Tukey-type transformations is investigated. Finally, results are compared to those of popular multi-parametric distribution models with closedform densities.
Subjects: 
kurtosis
skewness
variable transformation
transformed Gaussian
return data.
Document Type: 
Working Paper

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