Some Fundamental Properties of a Multivariate von Mises Distribution

Abstract

In application areas like bioinformatics, multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modeling of such situations is to use mixtures of unimodal distributions. In the literature (Mardia et al., 2012), the multivariate von Mises distribution, also known as the multivariate sine distribution, has been suggested for components of such models, but work in the area has been hampered by the fact that no good criteria for the von Mises distribution to be unimodal were available. In this article we study the question about when a multivariate von Mises distribution is unimodal. We give sufficient criteria for this to be the case and show examples of distributions with multiple modes when these criteria are violated. In addition, we propose a method to generate samples from the von Mises distribution in the case of high concentration.

Keywords:

• Bioinformatics
• Directional distributions
• Mixture models
• Modes
• Simulation
• Sine distribution

Mathematics Subject Classification:

• Primary 62H11
• Secondary 62H05, 62P99
• 62P10

Acknowledgments

The authors wish to thank John Kent for many helpful discussions.