Agreement Probabilities for Some CPIT - Neyman Smooth Tests

The CPIT transformations do not, in general, give the same set of transformed values for different orderings of the observations in a sample. When these transformations are followed by a test of uniformity to give an overall goodness-of-fit test, it is possible to obtain different results for different orderings of a sample. We consider here the probability that two goodness-of-fit tests based on randomly selected permutations of the same sample and a Neyman smooth uniformity test will . ~ agree in their conclusions. We observe for the cases considered in a simulation study that the probability of agreement is generally large and tends to one with increasing n.