Robust Normality Test in the Presence of Outliers

Abstract In classical statistics, detecting the normality of the data is one of the essential assumptions. However, if the selected random samples have some outliers, this assumption is violated. It is now evident that the Jarque-Bera (JB) test is one of the most powerful tests of normality. The study shows that in the presence of outliers, the JB test does not perform well in many situations. Thus, they proposed a robust Jarque-Bera (RJB) test as an alternative. In this article, we incorporate the idea of Gel and Gastwirth and proposed also a modified Jarque-Bera (MJB) test which has more power than the RJB. The results of the real-life example and simulation study shows that the power of MJB is higher in detecting normality of data compared to the JB and RJB test.