The L-distribution and skew generalizations

Matthias J. Fischer

No 75/2006, Discussion Papers from Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics

Abstract: Leptokurtic or platykurtic distributions can, for example, be generated by applying certain non-linear transformations to a Gaussian random variable. Within this work we focus on the class of so-called power transformations which are determined by their generator function. Examples are the H-transformation of Tukey (1960), the J-transformation of Fischer and Klein (2004) and the L-transformation which is derived from Johnson's inverse hyperbolic sine transformation. It is shown that generator functions themselves which meet certain requirements can be used to construct both probability densities and cumulative distribution functions. For the J-transformation, we recover the logistic distribution. Using the L-transformation, a new class of densities is derived, discussed and generalized.

Keywords: Power kurtosis transformation; leptokurtosis; (skew) L-distribution (search for similar items in EconPapers)
Date: 2006
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