Power kurtosis transformations: Definition, properties and ordering

Author： Klein Ingo  

Publisher： Springer Publishing Company

ISSN： 0002-6018

Source： Allgemeines Statistisches Archiv, Vol.90, Iss.3, 2006-09, pp. : 395-401

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Abstract

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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