A family of distributions on the m-sphere and some hypothesis tests

Abstract

SUMMARY A general class of distributions on the m -sphere is introduced and some properties of the class are noted. A subclass of this general class is shown to have interesting additional properties. Simple hypothesis tests (a) for randomness on the sphere, and (b) for the direction of the modal vector in the nonuniform case are suggested. The significance level of each test statistic and the power of the test are simple to compute.