The Annals of Statistics

Skewness and Asymmetry: Measures and Orderings

H. L. MacGillivray

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Abstract

Recent interest in skewness has tended to separate two aspects of the concept. Two distributions may be compared with respect to skewness, or a distribution may be self-compared, that is, the distributions of the random variables of X and - X may be compared. This paper uses the unification of these two aspects to attemp to complete a skewness structure of orderings that identifies the roles of various skewness and scale measures and enables classification of the skewness properties of any distribution. The structure is also used to propose measures of asymmetry. Some skewness properties of the Weibull and Johnson systems are examined.

Article information

Source
Ann. Statist., Volume 14, Number 3 (1986), 994-1011.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350046

Digital Object Identifier
doi:10.1214/aos/1176350046

Mathematical Reviews number (MathSciNet)
MR856802

Zentralblatt MATH identifier
0604.62011

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 60E05: Distributions: general theory

Keywords
Asymmetry skewness scale partial orderings of distributions mean median moments quantiles

Citation

MacGillivray, H. L. Skewness and Asymmetry: Measures and Orderings. Ann. Statist. 14 (1986), no. 3, 994--1011. doi:10.1214/aos/1176350046. https://projecteuclid.org/euclid.aos/1176350046


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Corrections

  • Correction: H. L. MacGillivray. Correction: Skewness and Asymmetry: Measures and Orderings. Ann. Statist., Volume 15, Number 2 (1987), 884.