Tests of normality: new test and comparative study

Abstract

This paper proposes a goodness of fit test of normality based on the common area under the empirical and theoretical distribution curves. Critical values of the proposed test are obtained via Monte Carlo simulations. The null distribution of the proposed test is approximated by Beta distribution. Power of the proposed test is studied and compared with that of the most familiar tests proposed in the literature, including: Kolmogrov-Smirnov, Anderson-Darling, Shapiro-Wilk, Shapiro-Francia, Cramer-von Mises, Watson, Kuiper, Vasicek’s, Park-Park test based on Vasicek’s estimator, Jarque-Bera, and Robust Jarque-Bera. Simulation results show that the proposed test is consistent and outperforms, in terms of power, the underlying tests in various scenarios.

Keywords:

• Empirical CDF
• GOF test
• normality tests
• Power
• Simulation

Acknowledgments

The author would like to thank the associate editor and two referees for their valuable comments and suggestions which had improved the earlier version of the paper.