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Biometrika 1980 67(2):455-461; doi:10.1093/biomet/67.2.455
© 1980 by Biometrika Trust
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A simple test for normality against asymmetric alternatives

CHING-CHUONG LIN and GOVTND S. MUDHOLKAR

Department of Mathematics, University of Maryland, Baltimore County
Department of Statistics, University of Rochester New York

The mean and the variance of a random sample are independently distributed if and only if the parent population is normal. This characterization is used as a basis for developing a test, termed the Z test, for the composite hypothesis of normality against asymmetric alternatives. The null distribution of the Z test statistic is for practical purposes satisfactorily approximated by a normal distribution for samples of size 5 up to 100. The large sample null distribution and the consistency of the test are also obtained. A Monte Carlo power study shows that the Z test has good power properties relative to some well-known competitors.

Key Words: Asymmetric distribution • Characterization • Independence • Monte Carlo • Skewness • Test for normality


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