On two simple tests for normality with high power

TL;DR

This paper introduces simplified versions of two high-power normality tests based on sample skewness and kurtosis, providing insights into their nature and making computations easier.

Contribution

It derives new test statistics for normality tests that are functions of skewness and kurtosis, enhancing understanding and computational efficiency.

Findings

New test statistics are functions of sample skewness and kurtosis.

The new tests are easier to compute than previous versions.

The tests maintain high power for normality detection.

Abstract

The test statistics of two powerful tests for normality \citep{lm1,mud2} are estimators of the correlation coefficient between certain sample moments. We derive new versions of the test statistics that are functions of the sample skewness and sample kurtosis. This sheds some light on the nature of these tests and leads to easier computations.