A goodness-of-fit test based on the empirical characteristic function and a comparison of tests for normality

Abstract: The normal distribution has the unique property that the cumulant generating function has only two terms, namely those involving the mean and the variance. This property is used to construct a simple by using the log of the modulus of the empirical characteristic function to what would be expected under normality. The test statistic is easy to calculate. Using a simulation study the proposed test is shown to have excellent power, especially in large samples.