Selecting the Best Population Using a Test for Equality Based on Minimal Wilcoxon Rank-sum Precedence Statistic |
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Authors: | Hon Keung Tony Ng N Balakrishnan S Panchapakesan |
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Institution: | (1) Department of Statistical Science, Southern Methodist University, Dallas, TX 75275-0332, USA;(2) Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada;(3) Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, IL 62901-4408, USA |
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Abstract: | In this paper, we first give an overview of the precedence-type test procedures. Then we propose a nonparametric test based
on early failures for the equality of two life-time distributions against two alternatives concerning the best population.
This procedure utilizes the minimal Wilcoxon rank-sum precedence statistic (Ng and Balakrishnan, 2002, 2004) which can determine the difference between populations based on early (100q%) failures. Hence, this procedure can be useful in life-testing experiments in biological as well as industrial settings.
After proposing the test procedure, we derive the exact null distribution of the test statistic in the two-sample case with
equal or unequal sample sizes. We also present the exact probability of correct selection under the Lehmann alternative. Then,
we generalize the test procedure to the k-sample situation. Critical values for some sample sizes are presented. Next, we examine the performance of this test procedure
under a location-shift alternative through Monte Carlo simulations. Two examples are presented to illustrate our test procedure
with selecting the best population as an objective.
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Keywords: | Two-sample problem k-sample problem Precedence statistics Life-testing Lehmann alternative Monte Carlo simulations Probability of correct selection Wilcoxon rank-sum statistic |
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