Multisample Tests for Multimodal and Axial Circular Populations

Abstract
We propose an l‐modal c‐sample non‐parametric test U on a circle based on uniform scores. The test is derived with the help of an l‐modal von Mises type distribution. Critical values of the distribution are given and the asymptotic distribution of U and its parametric competitor V are obtained. For the shift‐type alternatives we derive Bahadur's efficiency of the U‐test relative to the V‐test and consider some particular cases. We also examine the small sample powers of U and V for the von Mises type distributions. For von Mises populations, the power of the U‐test is studied in relation to the power of another reasonable non‐parametric test U'. We then indicate how these tests can be used for the axial case. Numerical examples are given to illustrate the use of the tests.

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