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An asymptotically distribution-free test of symmetry
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https://doi.org/10.1016/j.jspi.2006.06.009Abstract
A procedure, based on sample spacings, is proposed for testing whether a univariate distribution is symmetric about some unknown value. The proposed test is a modification of a sign test suggested by Antille and Kersting [1977. Tests for symmetry. Z. Wahrscheinlichkeitstheorie verw. Gebiete 39, 235-255], but unlike Antille and Kersting's test, our modified test is asymptotically distribution-free and is usable in practice. A simulation study indicates that the proposed test maintains the nominal level of significance, α fairly accurately even for samples of size as small as 20, and a comparison with the classical test based on sample coefficient of skewness, shows that our test has good power for detecting different asymmetric distributions. © 2006 Elsevier B.V. All rights reserved.
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