Goodness-of-Fit Tests Based on Kullback-Leibler Information

We evaluate the power of the sample entropy goodness-of-fit tests for s-normal, exponential, and uniform distributions. We compare them with the mainstream statistical tests, the W test based on the best linear unbiased estimator (BLUE) of the location parameter, the Z test based on the sample spacings, and the R test based on the correlation coefficient between the order statistics of the sample & the corresponding population quantiles. We show that the latter are more powerful overall. The mainstream statistical tests, particularly the Z test, readily extend to censored samples and to multi-sample situations.