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Two Powerful Tests for Normality

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  • Havva Alizadeh Noughabi

    (University of Gonabad)

Abstract

In this paper, two powerful tests for normality are proposed based on the Noughabi’s entropy estimator (J Stat Comput Simul 80:1151–1162, 2010). The power values of the proposed tests are computed and compared with the most popular normality test i.e., Shapiro–Wilk’s test. According to (Judge et al. in The theory and practice of econometrics, Wiley, New York, 1980) the Shapiro–Wilk statistic has become the most popular normality test because of its performance in Monte Carlo simulations. Moreover, the Shapiro–Wilks test is one of the tests used in SAS software for testing normality. Finally, some illustrative examples are presented and analyzed.

Suggested Citation

  • Havva Alizadeh Noughabi, 2016. "Two Powerful Tests for Normality," Annals of Data Science, Springer, vol. 3(2), pages 225-234, June.
    • Handle: RePEc:spr:aodasc:v:3:y:2016:i:2:d:10.1007_s40745-016-0083-y
    DOI: 10.1007/s40745-016-0083-y
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    References listed on IDEAS

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    1. Gel, Yulia R. & Miao, Weiwen & Gastwirth, Joseph L., 2007. "Robust directed tests of normality against heavy-tailed alternatives," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2734-2746, February.
    2. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    3. Zhang, Jin & Wu, Yuehua, 2005. "Likelihood-ratio tests for normality," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 709-721, June.
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    Cited by:

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    2. Lorentz Jäntschi & Sorana D. Bolboacă, 2018. "Computation of Probability Associated with Anderson–Darling Statistic," Mathematics, MDPI, vol. 6(6), pages 1-17, May.

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