Computational Statistics

, Volume 27, Issue 2, pp 299–317 | Cite as

Improved omnibus test statistic for normality

  • Shigekazu NakagawaEmail author
  • Hiroki Hashiguchi
  • Naoto Niki
Original Paper


We propose a new omnibus test statistic for normality based on the Jarque–Bera test statistic. We give the exact first four moments of the null distribution for the statistic using a computer algebra system. Our proposed statistic is an improvement of Jarque–Bera test statistic. Then the cumulants of the standardized statistic satisfy the Cornish–Fisher assumption. We give a normalizing transformation of the statistic based on the Wilson–Hilferty transformation.


Jarque–Bera test Kurtosis Normalizing transformation Powers Sampling moments Skewness 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Shigekazu Nakagawa
    • 1
    Email author
  • Hiroki Hashiguchi
    • 2
  • Naoto Niki
    • 3
  1. 1.Department of Computer Science and MathematicsKurashiki University of Science and the ArtsKurashikiJapan
  2. 2.Graduate School of Science and EngineeringSaitama UniversitySakuraJapan
  3. 3.Department of Management ScienceTokyo University of ScienceTokyoJapan

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