# von Mises

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MML
Continuous
von Mises

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.
 Coding Ockham's Razor, L. Allison, Springer A Practical Introduction to Denotational Semantics, L. Allison, CUP

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 © L. Allison   http://www.allisons.org/ll/   (or as otherwise indicated), Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University, was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.) Created with "vi (Linux + Solaris)",  charset=iso-8859-1,  fetched Thursday, 02-Feb-2023 05:33:20 AEDT.