[R] Von Mises mixtures: mu and kappa?

[Bert Gunter]

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Searching "von mises mixture distributions" on rseek.org brought up
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Cheers,
Bert


Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Tue, Feb 14, 2017 at 8:55 AM, Peter Mills <peter.mills at strath.ac.uk> wrote:
> Hello
>
> I am trying to calculate the values of the concentration parameters (kappa) and preferred direction (mu) for a Von Mises mixture model. I currently have some R code that gives me optimised values for the product of kappa and mu, but I'm not sure how to calculate them when both are unknown? How could I calculate mu and kappa from y2 if I didn't know either in the 1st place? I what to use movMF to give me values of kappa from some directional data where I don't know either kappa or mu.
>
>
> ## Generate and fit a "small-mix" data set a la Banerjee et al.
> mu <- rbind(c(-0.251, -0.968),
>             c(0.399, 0.917))
> kappa <- c(4, 4)
>
> theta <- kappa * mu
> theta
> alpha <- c(0.48, 0.52)
>
> ## Generate a sample of size n = 50 from the von Mises-Fisher mixture
> ## with the above parameters.
> set.seed(123)
> x <- rmovMF(50, theta, alpha)
> ## Fit a von Mises-Fisher mixture with the "right" number of components,
> ## using 10 EM runs.
> y2 <- movMF(x, 2, nruns = 10)
>
> Y2 gives
>> y2
> theta:
>        [,1]      [,2]
> 1  2.443225  5.259337
> 2 -1.851384 -4.291278
> alpha:
> [1] 0.4823648 0.5176352
> L:
> [1] 24.98124
>
> How could I calculate kappa and mu if I didn't know either in the 1st place?
>
> Thanks
> Peter
>
>
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