Selecting the Best Population Using a Test for Equality Based on Minimal Wilcoxon Rank-sum Precedence Statistic

Hon Keung Tony Ng (), N. Balakrishnan and S. Panchapakesan
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Hon Keung Tony Ng: Southern Methodist University
N. Balakrishnan: McMaster University
S. Panchapakesan: Southern Illinois University at Carbondale

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 2, 263-305

Abstract: 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.

Keywords: Two-sample problem; k-sample problem; Precedence statistics; Life-testing; Lehmann alternative; Monte Carlo simulations; Probability of correct selection; Wilcoxon rank-sum statistic; 62G10; 62N05 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s11009-007-9023-9

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