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An Omnibus Test for Univariate and Multivariate Normality


  • Jurgen A. Doornik
  • Henrik Hansen


We suggest a convenient version of the omnibus test for normality, using skewness and kurtosis based on Shenton and Bowman [Journal of the American Statistical Association (1977) Vol. 72, pp. 206–211], which controls well for size, for samples as low as 10 observations. A multivariate version is introduced. Size and power are investigated in comparison with four other tests for multivariate normality. The first power experiments consider the whole skewness–kurtosis plane; the second use a bivariate distribution which has normal marginals. It is concluded that the proposed test has the best size and power properties of the tests considered.

Suggested Citation

  • Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
  • Handle: RePEc:bla:obuest:v:70:y:2008:i:s1:p:927-939
    DOI: 10.1111/j.1468-0084.2008.00537.x

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    References listed on IDEAS

    1. D. R. Cox & Nanny Wermuth, 1994. "Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(2), pages 347-355, June.
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    4. Jean-Marie Dufour & Abdeljelil Farhat & Lucien Gardiol & Lynda Khalaf, 1998. "Simulation-based finite sample normality tests in linear regressions," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages 154-173.
    5. J. P. Royston, 1982. "The W Test for Normality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 176-180, June.
    6. Srivastava, M. S., 1984. "A measure of skewness and kurtosis and a graphical method for assessing multivariate normality," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 263-267, October.
    7. Bera, A. & John, S., 1983. "Tests for multivariate normality with Pearson alternatives," LIDAM Reprints CORE 534, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. J. P. Royston, 1982. "An Extension of Shapiro and Wilk's W Test for Normality to Large Samples," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(2), pages 115-124, June.
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