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Title:A note on the construction of generalized Tukey-type transformations PDF Logo
Authors:Fischer, Matthias J.
Issue Date:2006
Series/Report no.:Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 73/2006
Abstract: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 K-transformation of MacGillivray & Cannon (1997) or the J-transformation of Fischer & Klein (2004) may be used. Recently, Klein & Fischer (2006) proposed a very general power kurtosis transformation which includes the above-mentioned transformations as special cases. Unfortunately, their transformation requires an infinite number of unknown parameters to be estimated. In contrast, we introduce a very simple method to construct êexible kurtosis transformations. In particular, manageable superstructures are suggested in order to statistically discriminate between H-, J-and K-distributions (associated to H-, J- and K-transformations).
Subjects:Generalized kurtosis transformation
H-transformation
Document Type:Working Paper
Appears in Collections:Diskussionspapiere des Lehrstuhls für Statistik und Ökonometrie, FAU Erlangen-Nürnberg

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