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Wilcoxon‐type rank‐sum precedence tests: large‐sample approximation and evaluation
Author(s) -
Ng H. K. T.,
Balakrishnan N.
Publication year - 2002
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.478
Subject(s) - wilcoxon signed rank test , edgeworth series , mathematics , null hypothesis , rank (graph theory) , sample size determination , sample (material) , statistics
Wilcoxon‐type rank‐sum precedence tests are useful alternatives to the precedence life‐test proposed for testing the hypothesis that two lifetime distribution functions are equal. In this paper, we first derive the exact power function under the Lehmann alternative for these tests. We also note that the large‐sample normal approximation for the null distribution is not satisfactory in case of small or moderate sample sizes. Then, we develop an Edgeworth expansion to approximate the significance probabilities. Comparison of normal approximation and Edgeworth approximation for various sample sizes are provided. Finally, an example is presented for illustration. Copyright © 2002 John Wiley & Sons, Ltd.