A comparison of normality tests towards convoluted probability distributions

Abstract

Due to several normality tests, different studies have been conducted to compare their power through a Monte Carlo simulation. However, the data observed in practice are not as standard as the data used in the simulation studies but rather a combination of two or more distributions known as convoluted distribution. The power and Type I error of the six commonly used normality tests towards convoluted distributions were compared through a simulation study. The results showed that the Type I error and the power of all the test vary for different convoluted distributions and sample sizes. The Type I error of the Jarque–Bera (JB) test was found to be consistently high compared to the other tests. However, none of the tests have a Type I error rate that exceeds 6%. In general, all the normality tests considered have less power towards convoluted distribution, particularly for small sample sizes. However, the power of JB test towards convoluted distributions was found to be better compared to the other tests.