Monte Carlo comparison of seven normality tests

Abstract

This article studies seven different tests of normality. The tests in question are Kolmogorov–Smirnov, Anderson–Darling, Kuiper, Jarque–Bera, Cramer von Mises, Shapiro–Wilk, and Vasicek. Each test is described and power comparisons are made by using Monte Carlo computations under various alternatives. The results are discussed and interpreted separately.

Keywords:

• test of normality
• Monte Carlo simulation
• power of test

Acknowledgements

The authors express their appreciation to an anonymous referee and the Associate Editor whose comments improved this manuscript. Partial support from Ordered and Spatial Data Center of Excellence of Ferdowsi University of Mashhad is acknowledged.