A power comparison and simulation study of goodness-of-fit tests

Abstract

We give the results of a comprehensive simulation study of the power properties of prominent goodness-of-fit tests. For testing the normal N(μ,σ2), we propose a new omnibus goodness-of-fit statistic C which is a combination of the Shapiro–Wilk statistic W and the correlation statistic R. We show that the test of normality based on C is overall more powerful than other prominent goodness-of-fit tests and is effective against both symmetric as well as skew alternatives. We also show that the null distribution of C can be approximated by a four-moment F. For the exponential E(θ,σ), Tiku statistic Z (using sample spacings) and modified Anderson–Darling A are the most powerful. For testing other distributions, the statistics based on generalized sample spacings and the modified Anderson–Darling statistic provide the most powerful tests.