John D. Cook • 8/24/2026

The von Mises-Fisher distribution

This article discusses the von Mises-Fisher distribution, a generalization of the von Mises distribution to higher-dimensional spheres. It emphasizes the importance of normalization constants, which are expressed using modified Bessel functions. The post explains how the constant ensures the density integrates to 1, highlights the special case when p=2 (circle) and p=3 (Fisher distribution), and notes that for certain orders, Bessel functions reduce to elementary functions. It ties into previous discussions on Bessel functions and provides insight into probability density functions on spherical domains.

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#Von Mises Fisher Distribution #Probability Density #Normalization Constant