Arbeitspapier

The L-distribution and skew generalizations

to connected objects

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.

Language: Englisch

Bibliographic citation: Series: Diskussionspapier ; No. 63/2004

Classification: Wirtschaft

Subject: Power kurtosis transformation
leptokurtosis
(skew) L-distribution

Event: Geistige Schöpfung

(who): Fischer, Matthias J.

Event: Veröffentlichung

(who): Friedrich-Alexander-Universität Erlangen-Nürnburg, Lehrstuhl für Statistik und Ökonometrie

(where): Nürnberg

(when): 2004

Handle: http://hdl.handle.net/10419/29628

Last update: 10.03.2025, 11:45 AM CET

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Object type

Arbeitspapier

Associated

Fischer, Matthias J.
Friedrich-Alexander-Universität Erlangen-Nürnburg, Lehrstuhl für Statistik und Ökonometrie

Time of origin

2004

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