Von Mises Distribution

There is one shape parameter $\kappa >0$, with support $x\in \left[-\pi ,\pi \right]$. For values of $\kappa <100$ the PDF and CDF formulas below are used. Otherwise, a normal approximation with variance $1/\kappa$ is used. [Note that the PDF and CDF functions below are periodic with period $2\pi$. If an input outside $x\in \left[-\pi ,\pi \right]$ is given, it is converted to the equivalent angle in this range.]

where $I_k(\kappa )$ is a modified Bessel function of the first kind.

This can be used for defining circular variance.

Implementation: scipy.stats.vonmises