
The von Mises distribution is a "natural" distribution
for circular attributes,
e.g. angles, time of day, day of the year, phase of the moon, etc..
"The von Mises distribution M(μ,κ) has a
mean direction μ and concentration parameter κ.
For small κ it tends to a uniform distribution and
for large κ it tends to a Normal Distribution with
variance 1/κ." 
T. Edgoose, L. Allison & D. L. Dowe,
An MML Classification of Protein Sequences that knows about angles and sequences.
Pacific Symp. Biocomputing 98, pp.585596, Jan. 1998.
 Probability density:
 f(x  μ, κ) = (1/(2.π.I_{0}(κ))).exp(κ.cos(xμ))
 where I_{0}(κ) is a normalisation constant.
 Using a uniform prior on μ over [0, 2.π)
 and prior h_{3}(κ) = κ/(1+κ^{2})^{3/2}, then
 Fisher information:
 F(μ,κ)
 = N.κ.A(κ).N.{1A(κ)/κ(A(κ))^{2}}
 = N^{2}.κ.A(κ).{1A(κ)/κ(A(κ))^{2}}
 where I_{1}(κ) = d I_{0}(κ)/d κ
 and A(κ) = d log(I_{0}(κ))/d κ = I_{1}(κ)/I_{0}(κ)
Notes
 See the [bibliography]
for references on the von Mises distribution.

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