Multisample Tests for Multimodal and Axial Circular Populations
Kanti V. Mardia, Barrie D. Spurr · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1973
Summary 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.