Test for rotational symmetry of data from the Watson distribution defined on the hypersphere

The Watson distribution defined on the hypersphere is much used for modeling axial data. This distribution is rotationally symmetric about the modal axis. Then, in practice, before using the Watson distribution for modeling our data, it is better to test the hypothesis of rotational symmetry. For this purpose, we consider the test given by Prentice. In this paper, we determine the empirical power of this test, when data come from a Watson distribution vs. the alternative, where data come from a mixture of two Watson distributions.