Monte Carlo comparison of normality tests based on varentropy estimators

Abstract

Recently, Alizadeh and Shafaei [Alizadeh Noughabi H, Shafaei Noughabi M. Varentropy estimators with applications in testing uniformity. J Stat Comput Simul. 2023;93:2582–2599] introduced some estimators for varentropy of a continuous random variable. The present article applies these estimators and construct some tests for normality. Percentage points of the new test statistics are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, a real data set is used to illustrate the application of the proposed tests.

KEYWORDS:

• Varentropy estimator
• empirical distribution function
• testing normality
• percentage points
• Monte Carlo simulation
• test power

Acknowledgements

The authors are grateful to anonymous referees and the associate editor for providing some useful comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).