Skewness by Splitting the scale parameter

Klein I, Fischer M (2006)


Publication Language: English

Publication Type: Journal article, Original article

Publication year: 2006

Journal

Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles / Taylor & Francis

Book Volume: 35

Pages Range: 1159-1171

Journal Issue: 7

DOI: 10.1080/03610920600692730

Abstract

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.

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How to cite

APA:

Klein, I., & Fischer, M. (2006). Skewness by Splitting the scale parameter. Communications in Statistics-Theory and Methods, 35(7), 1159-1171. https://doi.org/10.1080/03610920600692730

MLA:

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

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