  In application areas like bioinformatics multivariate distributions on angles
are encountered which show significant clustering. One approach to statistical
modelling of such situations is to use mixtures of unimodal distributions. In
the literature (Mardia et al., 2011), 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.
