Improved omnibus test statistic for normality.

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. [ABSTRACT FROM AUTHOR]