Goodness-of-fit methods for the bipolar Watson distribution defined on the hypersphere

The Watson distribution is frequently used for modeling axial data. In this paper, we present goodness-of-fit methods for the bipolar Watson distribution defined on the hypersphere. We analyze by simulation some questions concerning these tests: the adequacy of the asymptotic chi-square distribution used in the tests and the adequacy of using the tabulated critical values for the Kolmogorov–Smirnov statistic when the parameters of the bipolar Watson distribution are unknown. We illustrate these techniques with simulated data from this distribution.