Skewness by Splitting the scale parameter

Journal article
(Original article)

Publication Details

Author(s): Klein I, Fischer M
Journal: Communications in Statistics-Theory and Methods
Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis
Publication year: 2006
Volume: 35
Journal issue: 7
Pages range: 1159-1171
ISSN: 0361-0926
Language: English


There are several possibilities for introducing skewness into a symmetric distribution. One of these procedures applies two different 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. Second, 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.

FAU Authors / FAU Editors

Fischer, Matthias Prof. Dr.
Fachbereich Wirtschaftswissenschaften
Klein, Ingo Prof. Dr.
Lehrstuhl für Statistik und Ökonometrie

How to cite

Klein, I., & Fischer, M. (2006). Skewness by Splitting the scale parameter. Communications in Statistics-Theory and Methods, 35(7), 1159-1171.

Klein, Ingo, and Matthias Fischer. "Skewness by Splitting the scale parameter." Communications in Statistics-Theory and Methods 35.7 (2006): 1159-1171.


Last updated on 2018-28-08 at 14:23