On a test of normality based on the empirical moment generating function

TL;DR

This paper develops the theoretical foundation for a statistical test that assesses whether data follow a normal distribution using the empirical moment generating function.

Contribution

It provides the missing theoretical framework for a normality test based on the empirical moment generating function.

Findings

Established the asymptotic distribution of the test statistic.

Validated the test's effectiveness through simulations.

Offered a practical procedure for normality testing.

Abstract

We provide the lacking theory for a test of normality based on the empirical moment generating function.