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

  • Hon Keung Tony Ng
  • N. Balakrishnan
  • S. Panchapakesan


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.


Two-sample problem k-sample problem Precedence statistics Life-testing Lehmann alternative Monte Carlo simulations Probability of correct selection Wilcoxon rank-sum statistic 

AMS 2000 Subject Classification

62G10 62N05 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Hon Keung Tony Ng
    • 1
  • N. Balakrishnan
    • 2
  • S. Panchapakesan
    • 3
  1. 1.Department of Statistical ScienceSouthern Methodist UniversityDallasUSA
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  3. 3.Department of MathematicsSouthern Illinois University at CarbondaleCarbondaleUSA

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