An approximation to the limit distribution of the epps-pulley test statistic for normality

Summary The approach of Epps and Pulley (1983) based on the empirical characteristic function is one of the most powerful tools for detecting any departures from normality. We obtain the first four moments of the limiting null distribution of the Epps-Pulley Statistic. Johnson- and Pearson curve fitting yields excellent approximations to simulated quantiles, and by modifying the test statistic the procedure may be carried out easily without the use of extensive tables for all sample sizes. Research done while the author was on leave at the University of Gie?en.