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Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) >
Lehrstuhl für Statistik und Ökonometrie, Universität Erlangen-Nürnberg >
Diskussionspapiere des Lehrstuhls für Statistik und Ökonometrie, FAU Erlangen-Nürnberg >
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http://hdl.handle.net/10419/29587
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| Title: | | Kurtosis modelling by means of the J-transformation  |
| Authors: | | Fischer, Matthias J. Klein, Ingo |
| Issue Date: | | 2003 |
| Series/Report no.: | | Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 51/2003 |
| 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 |
| Appears in Collections: | | Diskussionspapiere des Lehrstuhls für Statistik und Ökonometrie, FAU Erlangen-Nürnberg
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