Add support for univariate von Mises distribution

[jdrugo]

Adding a univariate von Mises distribution makes sense on top of the already available multivariante von Mises-Fisher distribution, if only for more efficient sampling from this distribution.

I have not yet included test scripts for this distribution, as doing so would require the use of circular statistics, which are not yet available in standard packages. The same applies to distribution fitting.

[simonbyrne]

I think this function would be more appropriate in Base.

[jdrugo]

Indeed, it should be in Base, but is not yet available. See JuliaLang/julia#6665

I have added it here temporarily, until it becomes available in Base.

[simonbyrne]

Rather than redefining these, you can just import them from Base.Math.

[lindahua]

@jdrugo Would you please incorporate latest changes in the master? Latest refactoring has substantial changes to many files, which makes this unmergeable in this form.

[jdrugo]

@lindahua I currently do not have access to my computer, but will update the files at the beginning of the next week.

[coveralls]

Coverage remained the same when pulling 54df12d on jdrugo:addvonmises into e200dc9 on JuliaStats:master.

[jdrugo]

The code is now updated in the light of the recent refactoring of Distributions.jl. It defines circmean, circvar, ... instead of mean, var, ... until a better solution is found (e.g. #224, even though this does not solve the issue of mean(rand(d, n)) not converging to mean(d) for large n).

Sampling from VonMises involves pre-computing some constants. Thus, it might make sense to write a separate VonMisesSampler. I can do this before a merge, if required.

[lindahua]

Yes, please add the sampler. My suggestion is

• add a samplers/vonmises.jl file, and introduce a sampler as

immutable VonMisesSampler <: Sampleable{Univariate,Continuous}
# cache some pre-computable quantities
...

function rand(s::VonMisesSampler)
     # move the sampling code here
end

and move the sampling code there.

• add a statement like the following in univariate/vonmises.jl:

sampler(d::VonMises) = VonMisesSampler( ... )

Other than that, it looks good to me.

[jdrugo]

I added both a VonMisesSampler and a VonMisesNormalApproxSampler for an efficient sampling of highly concentrated von Mises densities. Otherwise, the changes were implemented as suggested.

[coveralls]

Coverage remained the same when pulling eb5853f on jdrugo:addvonmises into e200dc9 on JuliaStats:master.

[lindahua]

Thanks!