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Biometrika 1969 56(3):561-570; doi:10.1093/biomet/56.3.561
© 1969 by Biometrika Trust
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The derivation of nonparametric two-sample tests from tests for uniformity of a circular distribution

R. J. BERAN

University of California Berkeley

Some recent developments in two-sample tests for shift alternatives on a circle and in tests for uniformity of a circular distribution are related in this paper. An intuitive correspondence, supported by formal analysis, is found between the two classes of test statistics in form, asymptotic null distribution and asymptotic behaviour under alternatives and leads to a method for constructing and inferring the properties of specific two-sample teats from the mathematically simpler tests for uniformity. Several useful two-sample tests on the circle, some previously suggested, the others new, are systematically derived.


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