New goodness-of-fit tests based on fiducial empirical distribution function

In this paper we derive new tests for goodness of fit based on the fiducial empirical distribution function (EDF) after the probability integral transformation of the sample. Note that the fiducial EDF for a set of given sample observations is a randomized distribution function. By substituting the fiducial EDF for the classical EDF in the Kolmogorov–Smirnov, Cramér–von Mises statistics and so forth, randomized statistics are derived, of which the qqth quantile and the expectation are chosen as test statistics. It emerges from Monte Carlo simulations that in most cases there exist some of the new tests having better power properties than the corresponding tests based on the classical EDF and Pyke’s modified EDF.