Simulation from a Matrix Fisher distribution on SO(3) {Directional}

Simulation from a Matrix Fisher distribution on SO(3)

Description

It simulates random samples (rotation matrices) from a Matrix Fisher distribution with any given parameter matrix, F (3x3).

Usage

rmatrixfisher(n, F)

Arguments

n

the sample size.

F

An arbitrary 3x3 matrix.

Details

Firstly corresponding Bingham parameter A is determined for a given Matrix Fisher parameter F using John Kent et al.'s (2013) algorithm and then Bingham samples for parameter A are generated using rbingham code. Finally convert Bingham samples to Matrix Fisher samples according to the Kent (2013) transformation.

Value

An array with simulated rotation matrices.

Author(s)

Anamul Sajib and Chris Fallaize.

R implementation and documentation: Anamul Sajib <[e-mail]> and Chris Fallaize.

References

Kent J. T., Ganeiber A. M. and Mardia K. V. (2018). A new unified approach for the simulation of a wide class of directional distributions. Journal of Computational and Graphical Statistics, 27(2): 291–301.

Kent J.T., Ganeiber A.M. and Mardia K.V. (2013). A new method to simulate the Bingham and related distributions in directional data analysis with applications. http://arxiv.org/pdf/1310.8110v1.pdf

See Also

matrixfisher.mle

Examples

F <- matrix( c(85, 11, 41, 78, 39, 60, 43, 64, 48), ncol = 3) / 10   ### An arbitrary F matrix
a <- rmatrixfisher(10, F)