A measure of skewness for testing departures from normality

TL;DR

This paper introduces a new skewness test statistic for assessing normality, utilizing the Pearson measure and Johnson $S_{U}$ system, with performance evaluated through power comparisons.

Contribution

It presents a novel skewness test statistic based on Pearson's measure and Johnson $S_{U}$ system, with derived moments and performance analysis.

Findings

The new test statistic has competitive power against alternatives.

Asymptotic moments of the null distribution are computed.

Performance comparison shows advantages over existing tests.

Abstract

We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing transformation based on the Johnson $S_{U}$ system. Finally the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses.