Discriminant analysis for a folded Watson distribution

When directional data fall in the positive orthant of the unit hypersphere, a folded directional distribution is preferred over a simple directional distribution for modeling the data. Since directional data, especially axial data, can be modeled using a Watson distribution, this paper considers a folded Watson distribution for such cases. We first address the parameter estimation of this distribution using maximum likelihood, which requires a numerical algorithm to solve the likelihood equations. We use the Expectation-Maximization (EM) algorithm to obtain these estimates and to analyze the properties of the concentration estimator through simulation. Next, we propose the Bayes rule for a folded Watson distribution and evaluate its performance through simulation in various scenarios, comparing it with the Bayes rule for the Watson distribution. Finally, we present examples using both simulated and real data available in the literature.