Comparative Analysis of the Powers of the Two-Sample Kolmogorov–Smirnov and Anderson–Darling Tests Under Various Alternatives

Abstract

In this paper we conduct a comparative analysis of the powers of the two-sample Kolmogorov–Smirnov and Anderson–Darling tests under various alternatives using simulation. We consider two examples. In the first example the alternatives to the standard normal distribution are the distributions of the so-called contaminated normal model. We study the influence of a small contamination with a positive shift on the powers of the test. In the second example the alternatives are the logistic and the Laplace distributions, which are symmetric and differ in shape from the normal distribution having a larger kurtosis coefficient and heavier tails.