Power comparisons of EDF goodness-of-fit tests

In this article, the power of common goodness-of-fit (GoF) statistics is based on the empirical distribution function (EDF) where the critical values must be determined by simulation. The statistical power of Kolmogorov–Smirnov $D_{n}$, Cramér-von Mises $W^{2}$, Watson $U^{2}$, Liao and Shimokawa $L_{n}$, and Anderson–Darling $A^{2}$ statistics were investigated by the sample size, the significance level, and the alternative distributions, for the generalized Rayleigh model (GR). The exponential, the Weibull, the inverse Weibull, the exponentiated Weibull, and the exponentiated exponential distributions were considered among the most frequent alternative distributions.