Power of some standard goodness-of-fit tests of normality against asymmetric stable alternatives

Erwin M. Saniga, James Alan Miles

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this article, we investigate the power of six standard goodness-of-fit tests of normality; several of these are sensitive to departures from normality in both skewness and kurtosis—the omnibus property. The power is estimated through simulation when the alternative is stable with α = 1.0(.3)1.9, β =.00(.25)1.00, and samples are of size n = 10, 20, 50, 100. The goodness-of-fit tests are based on the skewness statistic √b1, the kurtosis statistic b2, a joint test using √b1and b2, the Shapiro-Wilk W, the Studentized range test u, and the D’Agostino D. Our results indicate that the test based on b2is generally preferred if n ≥ 50 and β ≤.75. For the remaining configurations of n, α, and β, the test based on √b1is generally preferred.

Original languageEnglish (US)
Pages (from-to)861-865
Number of pages5
JournalJournal of the American Statistical Association
Volume74
Issue number368
DOIs
StatePublished - Jan 1 1979

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Test of Normality
Goodness of Fit Test
Alternatives
Skewness
Statistic
Kurtosis
Normality
Configuration
Standards
Goodness of fit test
Range of data
Simulation

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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Power of some standard goodness-of-fit tests of normality against asymmetric stable alternatives. / Saniga, Erwin M.; Miles, James Alan.

In: Journal of the American Statistical Association, Vol. 74, No. 368, 01.01.1979, p. 861-865.

Research output: Contribution to journalArticle

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