von Mises–Fisher distribution

Summary

The von Mises–Fisher distribution is a probability distribution on the unit sphere that is concentrated around a mean direction. Its density is proportional to $\exp(\kappa \mu^T x)$, where $\mu$ is the mean direction and $\kappa \ge 0$ controls the concentration. It plays the role of the normal distribution in directional statistics. On the circle it is the von Mises distribution, and on the ordinary sphere it is the Fisher distribution.