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September, 1986 Skewness and Asymmetry: Measures and Orderings
H. L. MacGillivray
Ann. Statist. 14(3): 994-1011 (September, 1986). DOI: 10.1214/aos/1176350046


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.


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H. L. MacGillivray. "Skewness and Asymmetry: Measures and Orderings." Ann. Statist. 14 (3) 994 - 1011, September, 1986.


Published: September, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0604.62011
MathSciNet: MR856802
Digital Object Identifier: 10.1214/aos/1176350046

Primary: 62E10
Secondary: 60E05

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 3 • September, 1986
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