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

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.