Abstract Constructing skew and heavy-tailed distributions by transform-ing a standard normal variable goes back to Tukey (1977) and was extended and formalized by Hoaglin (1983) and Martinez & Iglewicz (1984). Applica-tions of Tukey’s GH distribution family – which are composed by a skew-ness transformation G and a kurtosis transformation H – can be found, for instance, in financial, environmental or medical statistics. Recently, alter-native transformations emerged in the literature. Rayner & MacGillivray (2002b) discuss the GK distributions, where Tukey’s H-transformation is replaced by another kurtosis transformation K. Similarly, Fischer & Klein (2004) advocate the J-transformation which also produces heavy tails but – in contrast to Tukey’s H-transformation – still guarantees the existence of all moments. Within this work we present a very general kurtosis trans-formation which nests H-, K- and J-transformation and, hence, permits to discriminate between them. Applications to financial and teletraffic data are given.
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