Simulated random vectors following the von Mises-Fisher distribution with mean direction \(\mu_{x}=(1, 0, 0)\) and \(\mu_{y}=(1, 1, 1)\), and concentration parameter is \(\kappa = 3\).
bdvmf$x: A \(300 \times 3\) numeric matrix containing simulated von Mises-Fisher data.
bdvmf$group: A group index vector.
In directional statistics, the von Mises–Fisher distribution (named after Ronald Fisher and Richard von Mises), is a probability distribution on the \((p-1)\)-dimensional sphere in \(R^{p}\)
The parameters \(\mu\), and \(\kappa\), are called the mean direction and concentration parameter, respectively. The greater the value of \(\kappa\), the higher the concentration of the distribution around the mean direction \(\mu\),. The distribution is unimodal for \(\kappa\), and is uniform on the sphere for \(\kappa=0\).
Embleton, N. I. Fisher, T. Lewis, B. J. J. (1993). Statistical analysis of spherical data (1st pbk. ed.). Cambridge: Cambridge University Press. pp. 115–116. ISBN 0-521-45699-1.