A Goodness of Fit Test for Normality Based on the Empirical Moment Generating Function

In this article, we propose a test statistic for normality based on integrated weighted mean square distance between the true and the empirical moment generating functions. Simulation study shows that the power of the proposed test competes well with other prominent goodness of fit tests such as Anderson-Darling, Shapiro-Wilk, D'Agostino, and Epps-Pulley tests. In particular, when testing against stable distributions the proposed test is found to be more powerful than other tests for a wide range of values of the stable index parameter. Also, the test shows comparatively higher power when testing against symmetric distributions with kurtosis slightly higher than that of the normal distribution.