A Comparison among Twenty-Seven Normality Tests

Md. Siraj- Ud- Doulah

Abstract

This paper studies and compares the power of 27 normality tests via the Monte Carlo simulation of sample data generated from symmetric three short-tailed and three long-tailed, asymmetric three short-tailed and three long-tailed distributions under different sample sizes by using R codes. Our simulation results showed that for symmetric short-tailed Uniform (0, 1), t (10) and Beta (4, 4) distributions showed that the Agostino-Pearson K2, Jarque Bera and Kurtosis tests have better power; and Shapiro-Wilk, Cramer-Von Mises and Hegazy-Green 1 tests have lower power. For symmetric t (5), Laplace (0, 1) and Logistic (2, 1) long-tailed distributions, Robust Jarque Bera, Geary and Jarque Bera observed most powerful tests and Bonett-Seier Test, Chi-Square and Bonett-Seier tests were observed least powerful tests. Under asymmetric Weibull (2, 3), Gompertz (10, 0.002) and Gamma (1, 5) short-tailed distributions showed that the Shapiro Wilk, Kurtosis and Robust Jarque Bera test were highlighted as a more powerful test and the Cramer-Von Mises, Shapiro-Wilk and Hegazy-Green 1 tests were highlighted as a least powerful tests. Alternatively, the asymmetric Lognormal (0, 1), Exponential (1) and Chi-square (5) long-tailed distributions, the Shapiro-Wilk test was the most powerful test for all and Jarque-Bera, Hegazy-Green 1 and Bontemps-Meddahi tests were observed as the least powerful.Keywords: Normality test, skewness, kurtosis, ROC Curve, Monte Carlo simulation, Real Life atasetsCite this ArticleMd. Siraj Ud Doulah . A Comparisonamong Twenty Seven Normality TestsResearch & Reviews: Journal of Statistics .2019; 8(3): 4 1 59 p.