Abstract
This chapter focuses on non-parametric tests. The chapter presents some appropriate analogues of important non-parametric tests on the line when the underlying populations are continuous. As there is no unique way of ordering a sample on the circle, the circular analogues are taken to be invariant under rotations. The chapter discusses tests for samples from multimodal and axial populations. The tests of goodness of fit on the circle are frequently used to test the hypothesis of uniformity. The Kolmogorov-type test, Kuiper's test, the Cramér-von Mises type test, Watson's U2 test, and Hodges–Ajne's test are reviewed in the chapter. The chapter also discusses the range test, a test of equal spacings, Beran's class of tests of uniformity, and Ajne's An-test. Hodges–Ajne's test and the range test provide two quick methods of assessing uniformity. To test the hypothesis that the zero direction is the axis of symmetry against the alternative of a displaced axis, the usual tests of symmetry on the line are used.
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