A Generalization of Ahmad's Class of Mann–Whitney–Wilcoxon Statistics |
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Authors: | Ömer Öztürk |
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Institution: | Dept of Statistics, Ohio State University, USA |
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Abstract: | In the spirit of the recent work of Ahmad (1996) this paper introduces another class of Mann–Whitney–Wilcoxon test statistics. The test statistic compares the r th and s th powers of the tail probabilities of the underlying probability distributions. The choice of r + s = 4 improves the Pitman efficiency for uniform, exponential, lognormal and normal distributions and keeps the same efficiency as the Mann–Whitney–Wilcoxon test for logistic and double exponential distributions. The two-sample test is modified for the one-sample problem with symmetric underlying distribution. |
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Keywords: | distribution-free non-parametric test Pitman efficiency stochastic ordering two-sample test U-statistic |
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