Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/29587 
Year of Publication: 
2003
Series/Report no.: 
Diskussionspapier No. 51/2003
Publisher: 
Friedrich-Alexander-Universität Erlangen-Nürnburg, Lehrstuhl für Statistik und Ökonometrie, Nürnberg
Abstract: 
The H-family of distributions or H-distributions, introduced by Tukey (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 leptokurtic distributions by applying the K-transformation to the normal distribution. In this study we propose a third transformation - the so-called J-transformation - and derive some properties of this transformation. Moreover, so-called elongation generating functions (EGF’s) are introduced. By means of EGF's we are able to visualize the strength of tail elongation and to construct new transformations. Finally, we compare the three transformations towards their goodness-of-fit in the context of financial return data.
Subjects: 
kurtosis
variable transformation
normal transformation
tail elongation.
Document Type: 
Working Paper

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