A Simple Empirical Likelihood Ratio Test for Normality Based on the Moment Constraints of a Half-Normal Distribution

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A simple and efficient empirical likelihood ratio (ELR) test for normality based on moment constraints of the half-normal distribution was developed. The proposed test can also be easily modified to test for departures from half-normality and is relatively simple to implement in various statistical packages with no ordering of observations required. Using Monte Carlo simulations, our test proved to be superior to other well-known existing goodness-of-fit (GoF) tests considered under symmetric alternative distributions for small to moderate sample sizes. A real data example revealed the robustness and applicability of the proposed test as well as its superiority in power over other common existing tests studied.