vmf: MLE of von Mises-Fisher distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/vmf.R

Description

MLE of the von Mises-Fisher distribution.

Usage

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vmf(x, fast = FALSE, tol = 1e-07)

Arguments

x

A matrix with the data expressed in Euclidean coordinates, i.e. unit vectors.

fast

A boolean variable to do a faster implementation.

tol

The tolerance to accept that the E-M algorithm used to estimate the concentration parameter has converged.

Details

The mean direction and concentration of a fitted von Mises-Fisher distribution are estimated.

Value

If fast = FALSE a list including all the following. If fast = TRUE less items are returned.

mu

The mean direction.

kappa

The concentration parameter.

MRL

The mean resultant length.

vark

The variance of the concentration parameter.

loglik

The maximum log-likelihood value.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[email protected]> and Giorgos Athineou <[email protected]>

References

Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

Sra, S. (2012). A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of Is(x). Computational Statistics, 27(1): 177–190.

See Also

iag.mle, rvmf, kent.mle, vmf.kde, wood.mle

Examples

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m <- rnorm(3)
m <- m/sqrt(sum(m^2))
m
x <- rvmf(100, m, 7)
vmf(x)
x <- rvmf(500, m, 7)
vmf(x)

Example output

[1] -0.67179829 -0.06453921  0.73791716
$mu
[1] -0.69434025 -0.06012674  0.71713067

$kappa
[1] 7.082554

$MRL
[1] 0.8588094

$vark
[1] 0.07082685

$loglik
[1] -88.02318

$mu
[1] -0.67605567 -0.07915935  0.73258619

$kappa
[1] 7.125117

$MRL
[1] 0.8596527

$vark
[1] 0.01425048

$loglik
[1] -437.1205

Directional documentation built on Nov. 12, 2018, 5:05 p.m.