A new empirical likelihood ratio goodness of fit test for normality based on moment constraints

A new empirical likelihood ratio test for normality based on moment relations is outlined. The proposed test is developed following the works of Shan et al. (2010 Shan, G., A. Vexler, G. E. Wilding, and A. D. Hutson. 2010. Simple and exact empirical likelihood ratio tests for normality based on moment relations. Communications in Statistics - Simulation and Computation 40 (1):129–46. doi:10.1080/03610918.2010.532896.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Our proposed test is simple and efficient and it is easy to implement in various statistical packages with the computation of the test statistic not requiring ordering of observations. Monte Carlo simulations revealed that the proposed test proved to be superior under asymmetric alternatives considered as well as symmetric alternatives defined on (0,1). Real data examples are given as well as recommendations of future research areas.