Von Mises Distribution

The von Mises distribution is a continuous probability distribution defined on a circle rather than a line, and it works as the basic tool of directional statistics, the branch of statistics dealing with angles and other circular data. It is also called the circular normal distribution or the Tikhonov distribution, and it closely approximates the wrapped normal distribution, acting as the circular version of the ordinary normal distribution. It has two parameters, a mean direction and a concentration parameter that plays a role similar to inverse variance, and it describes an angle that drifts and diffuses around the circle under a directional pull. It is the distribution that carries the most entropy among circular distributions once the real and imaginary parts of the first circular moment are fixed. When its concentration parameter is large the distribution looks close to a normal distribution, and when that parameter approaches zero it becomes the uniform distribution on the circle; it generalizes to higher dimensions through the von Mises-Fisher distribution on spheres.