Power kurtosis transformations: Definition, properties and ordering |
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Authors: | Ingo Klein and Matthias Fischer |
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Institution: | (1) Lehrstuhl für Statistik und ?konometrie, Universit?t Erlangen-Nürnberg, Lange Gasse 20, D-90403 Nürnberg |
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Abstract: | Summary Heavy tail distributions can be generated by applying specific non-linear transformations to a Gaussian random variable. Within
this work we introduce power kurtosis transformations which are essentially determined by their generator function. Examples
are theH-transformation of Tukey (1960), theK-transformation of MacGillivray and Cannon (1997) and theJ-transformation of Fischer and Klein (2004).Furthermore, we derive a general condition on the generator function which guarantees
that the corresponding transformation is actually tail-increasing. In this case the exponent of the power kurtosis transformation
can be interpreted as a kurtosis parameter. We also prove that the transformed distributions can be ordered with respect to
the partial ordering of van Zwet (1964) for symmetric distributions. |
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Keywords: | Power kurtosis transformation leptokurtosis kurtosis ordering JEL C16 C51 |
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