Multi-Sample Likelihood Ratio Tests Based on Bipolar Watson Distributions Defined on the Hypersphere

Abstract

We derive likelihood ratio tests for the equality of the directional parameters of k bipolar Watson distributions defined on the hypersphere with common concentration parameter. We analyze the power of these tests in the case of two distributions supposing in the alternative hypothesis two directional parameters forming an angle, which varies from 18° to 90°. We also compare the likelihood ratio tests with a high-concentration F-test.

Keywords:

• Directional data
• Likelihood ratio tests
• Multi-sample tests
• Watson distribution

Mathematics Subject Classification:

• Primary 62H11
• Secondary 62H15