A New Test for Normality Based on Balakrishnan – Sanghvi Divergence Measure

In this paper, a more robust estimator of the Shannon entropy is applied in place of an earlier estimator, to obtain an improved goodness-of-fit test to normality which is based on the Balakrishnan-Sanghvi measure of divergence. The statistic is affine invariant and consistent against fixed alternatives. The critical values of the new statistic and those of a competing statistic as well as their power comparisons are obtained through extensive simulation study. The result of the power comparison showed that the statistic can be recommended as a good test for normality especially at small samples and against symmetric alternative distributions.