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December, 1977 A Local Limit Theorem for the Wilcoxon Rank Sum
Daniel Thorburn
Ann. Probab. 5(6): 926-939 (December, 1977). DOI: 10.1214/aop/1176995661


The normalized probability function of the Wilcoxon rank sum statistic is shown to converge to the normal density under very mild conditions on the two sample distributions. This is done by studying the conditional distribution of the rank sum given the first sample and by a rather heavy use of characteristic functions.


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Daniel Thorburn. "A Local Limit Theorem for the Wilcoxon Rank Sum." Ann. Probab. 5 (6) 926 - 939, December, 1977.


Published: December, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0376.60035
MathSciNet: MR461776
Digital Object Identifier: 10.1214/aop/1176995661

Primary: 60F99
Secondary: 62G99

Keywords: local limit theorem , Mann-Whitney , rank sum , Wilcoxon

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • December, 1977
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