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Title:Skewness by splitting the scale parameter PDF Logo
Authors:Klein, Ingo
Fischer, Matthias J.
Issue Date:2003
Series/Report no.:Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 55/2003
Abstract:There are several possibilities to introduce skewness into a symmetric distribution. One of these procedures applies two dfferent parameters of scale - with possibly different weights - to the positive and the negative part of a symmetric density. Within this work we show that this technique incorporates a well-defined parameter of skewness, i.e. that the generated distributions are skewed to the right (left) if the parameter of skewness takes values less (greater) than one. Secondly, we prove that the skewness parameter is compatible with the skewness ordering of van Zwet (1964) which is the strongest ordering in the hierarchy of orderings discussed by Oja (1981). Hence, the generated (skewed) distributions can be ordered by the skewness parameter.
Subjects:Skewness
skewness to the right
skewness ordering
score function.
Document Type:Working Paper
Appears in Collections:Diskussionspapiere des Lehrstuhls für Statistik und Ökonometrie, FAU Erlangen-Nürnberg

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