Kurtosis modelling by means of the J-transformation

Matthias J. Fischer and Ingo Klein

No 51/2003, Discussion Papers from Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics

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.

Keywords: kurtosis; variable transformation; normal transformation; tail elongation. (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (1)

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