Multisample Tests for Multimodal and Axial Circular Populations
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1973 · Volume 35 · Issue 3
DOI: 10.1111/j.2517-6161.1973.tb00970.x
Abstract
We propose anl-modalc-sample non-parametric testUon a circle based on uniform scores. The test is derived with the help of anl-modal von Mises type distribution. Critical values of the distribution are given and the asymptotic distribution ofUand its parametric competitorVare obtained. For the shift-type alternatives we derive Bahadur's efficiency of theU-test relative to theV-test and consider some particular cases. We also examine the small sample powers ofUandVfor the von Mises type distributions. For von Mises populations, the power of theU-test is studied in relation to the power of another reasonable non-parametric testU'.We then indicate how these tests can be used for the axial case. Numerical examples are given to illustrate the use of the tests.
Keywords
a.r.e. of circular tests, multimodal and axial distributions, uniform circular scores, von mises distribution
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