**Definition**

The von Mises probability density function for the angle *x* is given by:

where *I*_{0}(*x*) is the modified Bessel function of order 0.

The parameters μ and 1/κ are analogous to μ and *σ**2* (the mean and variance) in the normal distribution:

- μ is a measure of location (the distribution is clustered around μ), and
- κ is a measure of concentration (a reciprocal measure of dispersion, so 1/κ is analogous to
*σ**2*).- If κ is zero, the distribution is uniform, and for small κ, it is close to uniform.
- If κ is large, the distribution becomes very concentrated about the angle μ with κ being a measure of the concentration. In fact, as κ increases, the distribution approaches a normal distribution in
*x*with mean μ and variance 1/κ.

The probability density can be expressed as a series of Bessel functions (see Abramowitz and Stegun §9.6.34)

where *I*_{j}(*x*) is the modified Bessel function of order *j*. The cumulative distribution function is not analytic and is best found by integrating the above series. The indefinite integral of the probability density is:

The cumulative distribution function will be a function of the lower limit of integration *x*_{0}:

Read more about this topic: Von Mises Distribution

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