A Test for Normality in the Presence of Outliers

The jarque-bera test is a test based on the coefficients of skewness (s) and kurtosis (k) for testing whether the given random sample is from a normal population. when the random sample of size n contains m outliers, we use the remaining n-m observations to compute two statistics s* and k* which mimic the statistics s and k. the statistics s* and k* are next transformed to z1 and z2 which are uncorrelated and having standard normal distributions when the original population is normal. we show that the acceptance region given by a circle in the (z1, z2) plane is suitable for testing the normality assumption.