Directional (version 4.0)

MLE of the von Mises-Fisher distribution: MLE of von Mises-Fisher distribution

Description

MLE of the von Mises-Fisher distribution.

Usage

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

Arguments

x

A matrix or an FBM matrix (Filebacked Big Matrix, for big data) with the data expressed in Euclidean coordinates, i.e. unit vectors.

fast

A boolean variable to do a slightly faster implementation. This does not support Filebacked Big Matrix.

tol

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

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.

Details

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

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

# NOT RUN {
m <- rnorm(3)
m <- m/sqrt(sum(m^2))
m
x <- rvmf(100, m, 7)
vmf(x)
x <- rvmf(500, m, 7)
vmf(x)
# }