# matrixfisher.mle: MLE of the Matrix Fisher distribution on SO(3) In Directional: A Collection of Functions for Directional Data Analysis

## Description

It returns the maximum likelihood estimate of the Matrix Fisher parameter F(3x3).

## Usage

 1 matrixfisher.mle(X) 

## Arguments

 X An array containing rotation matrices in SO(3).

## Value

The components of svd( \bar(X) ) .

## Author(s)

Anamul Sajib & Chris Fallaize.

R implementation and documentation: Anamul Sajib <sajibstat@du.ac.bd> & Chris Fallaize.

## References

Prentice M. J. (1986). Orientation statistics without parametric assumptions.Journal of the Royal Statistical Society. Series B: Methodological 48(2).

rmatrixfisher 

## Examples

 1 2 3 4 F <- 10^(-1) * matrix( c(85, 11, 41, 78, 39, 60, 43, 64, 48), ncol = 3 ) ### An arbitrary F matrix X <- rmatrixfisher(5000, F) matrixfisher.mle(X) svd(F) 

### Example output

$d [1] 0.9438542 0.8438829 0.8350391$u
[,1]       [,2]       [,3]
[1,] -0.7438811  0.5417791 -0.3913008
[2,] -0.4017843 -0.8304240 -0.3859603
[3,] -0.5340507 -0.1298900  0.8354151

$v [,1] [,2] [,3] [1,] -0.5475900 0.6703522 0.5007725 [2,] -0.6582875 0.0243105 -0.7523740 [3,] -0.5165296 -0.7416448 0.4279723$d
[1] 16.1689380  4.8012212  0.5689634

$u [,1] [,2] [,3] [1,] -0.7437561 0.5476574 -0.3832731 [2,] -0.3992959 -0.8238324 -0.4023219 [3,] -0.5360873 -0.1461900 0.8314077$v
[,1]        [,2]       [,3]
[1,] -0.5540939  0.65597751 -0.5125167
[2,] -0.6540365  0.03783228  0.7555164
[3,] -0.5149914 -0.75383170 -0.4080706


Directional documentation built on Nov. 8, 2021, 1:07 a.m.