# vmf: MLE of von Mises-Fisher distribution In Directional: Directional Statistics

## Description

MLE of the von Mises-Fisher distribution.

## Usage

 `1` ```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.

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

## Examples

 ```1 2 3 4 5 6 7``` ```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.