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

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)N(μ,σ2), we propose a new omnibus goodness-of-fit statistic CC which is a combination of the Shapiro–Wilk statistic WW and the correlation statistic RR. We show that the test of normality based on CC 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 CC can be approximated by a four-moment FF. For the exponential E(θ,σ)E(θ,σ), Tiku statistic ZZ (using sample spacings) and modified Anderson–Darling AA 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.