Some nonparametric precedence-type tests based on progressively censored samples and evaluation of power |
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Authors: | N Balakrishnan RC Tripathi N Kannan HKT Ng |
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Institution: | 1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1;2. Department of Management Science and Statistics, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA;3. Department of Statistical Science, Southern Methodist University, Dallas, TX 75275-0332, USA |
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Abstract: | In this paper, we consider the problem of testing the equality of two distributions when both samples are progressively Type-II censored. We discuss the following two statistics: one based on the Wilcoxon-type rank-sum precedence test, and the second based on the Kaplan–Meier estimator of the cumulative distribution function. The exact null distributions of these test statistics are derived and are then used to generate critical values and the corresponding exact levels of significance for different combinations of sample sizes and progressive censoring schemes. We also discuss their non-null distributions under Lehmann alternatives. A power study of the proposed tests is carried out under Lehmann alternatives as well as under location-shift alternatives through Monte Carlo simulations. Through this power study, it is shown that the Wilcoxon-type rank-sum precedence test performs the best. |
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Keywords: | primary: 62G10 62N05 secondary: 62P30 |
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