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

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  • Hon Keung Tony Ng

    (Southern Methodist University)

  • N. Balakrishnan

    (McMaster University)

  • S. Panchapakesan

    (Southern Illinois University at Carbondale)

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.

Suggested Citation

  • Hon Keung Tony Ng & N. Balakrishnan & S. Panchapakesan, 2007. "Selecting the Best Population Using a Test for Equality Based on Minimal Wilcoxon Rank-sum Precedence Statistic," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 263-305, June.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:2:d:10.1007_s11009-007-9023-9
    DOI: 10.1007/s11009-007-9023-9
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    References listed on IDEAS

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    1. Paul Laan & Subha Chakraborti, 2001. "Precedence tests and Lehmann alternatives," Statistical Papers, Springer, vol. 42(3), pages 301-312, July.
    2. H. K. T. Ng & N. Balakrishnan, 2002. "Wilcoxon‐type rank‐sum precedence tests: large‐sample approximation and evaluation," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 18(3), pages 271-286, July.
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    Cited by:

    1. Alexander E. Plesovskikh, 2023. "Special Economic Zones of Russia: Forecasting Decisions of Potential Residents and Resident Generation Process Modeling," Journal of Applied Economic Research, Graduate School of Economics and Management, Ural Federal University, vol. 22(2), pages 323-354.

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