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A note on the construction of generalized Tukey-type transformations

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  • Fischer, Matthias J.

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).

Suggested Citation

  • Fischer, Matthias J., 2006. "A note on the construction of generalized Tukey-type transformations," Discussion Papers 73/2006, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:732006
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    References listed on IDEAS

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    1. Ingo Klein & Matthias Fischer, 2006. "Power kurtosis transformations: Definition, properties and ordering," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(3), pages 395-401, September.
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