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A Generalization of Ahmad's Class of Mann–Whitney–Wilcoxon Statistics

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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 rth and sth 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: Pitman efficiency; U-statistic; distribution-free; non-parametric test; stochastic ordering; two-sample test

Document Type: Research Article

Affiliations: Dept of Statistics, Ohio State University, USA

Publication date: March 1, 2001

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