Von Mises–Fisher distribution

In directional statistics, the von Mises–Fisher distribution (named after Ronald Fisher and Richard von Mises), is a probability distribution on the ${\displaystyle (p-1)}$-dimensional sphere in ${\displaystyle \mathbb {R} ^{p}}$. If ${\displaystyle p=2}$ the distribution reduces to the von Mises distribution on the circle.

The probability density function of the von Mises–Fisher distribution for the random p-dimensional unit vector ${\displaystyle \mathbf {x} \,}$ is given by:

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