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March, 1979 The Small Sample Distribution of a Mann-Whitney Type Statistic for Circular Data
W. J. R. Eplett
Ann. Statist. 7(2): 446-453 (March, 1979). DOI: 10.1214/aos/1176344626

Abstract

The union-intersection method of test construction can be used to derive from the Mann-Whitney rank test a test statistic for testing whether two samples of observations from circular distributions come from the same population. The null distribution of this test statistic will be investigated here. The approach followed is to use the principle of inclusion-exclusion to obtain an expression for the number of partitions of a positive integer which satisfy certain conditions. This enables the probabilities for values of the circular Mann-Whitney test statistic to be expressed explicitly in terms of the probabilities for values of the usual Mann-Whitney test statistic. Recurrence formulae enabling computation of the distribution for small sample sizes are given. There is a clear relationship between our work and results obtained by Steck for the Kolmogorov and Smirnov statistics. These results can also be derived from the present approach.

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W. J. R. Eplett. "The Small Sample Distribution of a Mann-Whitney Type Statistic for Circular Data." Ann. Statist. 7 (2) 446 - 453, March, 1979. https://doi.org/10.1214/aos/1176344626

Information

Published: March, 1979
First available in Project Euclid: 12 April 2007

zbMATH: 0414.62036
MathSciNet: MR520252
Digital Object Identifier: 10.1214/aos/1176344626

Subjects:
Primary: 62G10
Secondary: 05A15 , 05A17

Keywords: determinant , generating function , Mann-Whitney rank test , principle of inclusion-exclusion , recurrence relation , Smirnov statistics

Rights: Copyright © 1979 Institute of Mathematical Statistics

Vol.7 • No. 2 • March, 1979
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