Distance-based hypothesis tests on the Watson distribution

Abstract

Directional data are related to vectors on the unit sphere. When these vectors are not signed, this kind of data is called axial data. The Watson distribution is one of the main models for axial data. This model is equipped by two parameters: dominant axis and concentration. Based on the Rényi divergence and the Bhattacharya and Hellinger distances, we propose three hypothesis tests to check if two samples come from populations having the same concentration parameter. Results from synthetic and real data indicate that the proposed tests can yield good performance on Watson data.

Keywords:

• Divergence-based statistics
• Watson distribution
• Unit sphere
• Kummer function

CLASSCODE:

• 62E20
• 62Fxx
• 94A17

Acknowledgments

This work was supported by CNPq and FACEPE, Brazil.