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Normality testing: two new tests using L-moments

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  • Ardian Harri
  • Keith H. Coble

Abstract

Establishing that there is no compelling evidence that some population is not normally distributed is fundamental to many statistical inferences, and numerous approaches to testing the null hypothesis of normality have been proposed. Fundamentally, the power of a test depends on which specific deviation from normality may be presented in a distribution. Knowledge of the potential nature of deviation from normality should reasonably guide the researcher's selection of testing for non-normality. In most settings, little is known aside from the data available for analysis, so that selection of a test based on general applicability is typically necessary. This research proposes and reports the power of two new tests of normality. One of the new tests is a version of the R -test that uses the L-moments, respectively, L-skewness and L-kurtosis and the other test is based on normalizing transformations of L-skewness and L-kurtosis. Both tests have high power relative to alternatives. The test based on normalized transformations, in particular, shows consistently high power and outperforms other normality tests against a variety of distributions.

Suggested Citation

  • Ardian Harri & Keith H. Coble, 2011. "Normality testing: two new tests using L-moments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1369-1379, May.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:7:p:1369-1379
    DOI: 10.1080/02664763.2010.498508
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    References listed on IDEAS

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    1. Paul Zhang, 1999. "Omnibus test of normality using the Q statistic," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(4), pages 519-528.
    2. Bonett, Douglas G. & Seier, Edith, 2002. "A test of normality with high uniform power," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 435-445, September.
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    Cited by:

    1. Andrea Bastianin, 2020. "Robust measures of skewness and kurtosis for macroeconomic and financial time series," Applied Economics, Taylor & Francis Journals, vol. 52(7), pages 637-670, February.
    2. Bastianin, Andrea & Manera, Matteo, 2021. "A test of symmetry based on L-moments with an application to the business cycles of the G7 economies," Economics Letters, Elsevier, vol. 198(C).
    3. Norbert Henze & Stefan Koch, 2020. "On a test of normality based on the empirical moment generating function," Statistical Papers, Springer, vol. 61(1), pages 17-29, February.

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