Powers of Discrete Goodness-of-Fit Test Statistics for a Uniform Null Against a Selection of Alternative Distributions

摘要

The comparative powers of six discrete goodness-of-fit test statistics for a uniform null distribution against a variety of fully specified alternative distributions are discussed. The results suggest that the test statistics based on the empirical distribution function for ordinal data (Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling) are generally more powerful for trend alternative distributions. The test statistics for nominal (Pearson's chi-square and the nominal Kolmogorov-Smirnov) and circular data (Watson's test statistic) are shown to be generally more powerful for the investigated triangular (∨), flat (or platykurtic type), sharp (or leptokurtic type), and bimodal alternative distributions.