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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.585-596, Jan. 1998.
- Probability density:
- f(x | μ, κ) = (1/(2.π.I0(κ))).exp(κ.cos(x-μ))
- where I0(κ) is a normalisation constant.
- Using a uniform prior on μ over [0, 2.π)
- and prior h3(κ) = κ/(1+κ2)3/2, then
- Fisher information:
- F(μ,κ)
- = N.κ.A(κ).N.{1-A(κ)/κ-(A(κ))2}
- = N2.κ.A(κ).{1-A(κ)/κ-(A(κ))2}
- where I1(κ) = d I0(κ)/d κ
- and A(κ) = d log(I0(κ))/d κ = I1(κ)/I0(κ)
Notes
- See the [bibliography]
for references on the von Mises distribution.
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