What is the name for this distribution defined on a circle

Question

One can define the probability distribution: $$ p(\theta; \alpha, \theta_0) = \frac{ e^{ \alpha \cos( \theta-\theta_0) }}{ 2 \pi I_0(\alpha)} $$ over an angular variable $\theta \in [0,2 \pi]$. By what name(s) is this distribution called?

($I_0$ is the modified Bessel function and serves to normalize the distribution)

Could you please define $I_0(\alpha)$? – Sycorax Oct 22 '13 at 15:17 — Sycorax, Oct 22 '13 at 15:17

score 5 · Accepted Answer · answered Oct 22 '13 at 15:17

5

It's von Mises distribution, aka Tikhonov distribution, and plays the role similar to the normal distribution in 1D statistics.

For reference, $I_0(z)$ is the modified Bessel function of order 0.

answered Oct 22 '13 at 15:17

StasK

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What is the name for this distribution defined on a circle

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