Directional (version 6.1)

Simulation of random values from rotationally symmetric distributions: Simulation of random values from rotationally symmetric distributions

Description

Simulation of random values from rotationally symmetric distributions. The data can be spherical or hyper-spherical.

Usage

rvmf(n, mu, k)
riag(n, mu)

Value

A matrix with the simulated data.

Arguments

n

The sample size.

mu

A unit vector showing the mean direction for the von Mises-Fisher distribution. The mean vector of the Independent Angular Gaussian distribution. This does not have to be a unit vector.

k

The concentration parameter of the von Mises-Fisher distribution. If k = 0, random values from the spherical uniform will be drwan.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris and Giorgos Athineou <[e-mail]>.

Details

The von Mises-Fisher uses the rejection smapling suggested by Wood (1994). For the Independent Angular Gaussian, values are generated from a multivariate normal distribution with the given mean vector and the identity matrix as the covariance matrix. Then each vector becomes a unit vector.

References

Wood A.T.A. (1994). Simulation of the von Mises Fisher distribution. Communications in Statistics-Simulation and Computation, 23(1): 157--164.

Dhillon I. S. & Sra S. (2003). Modeling data using directional distributions. Technical Report TR-03-06, Department of Computer Sciences, The University of Texas at Austin. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.75.4122&rep=rep1&type=pdf

See Also

vmf.mle, iag.mle rfb, racg, rvonmises, rmixvmf

Examples

m <- rnorm(4)
m <- m/sqrt(sum(m^2))
x <- rvmf(100, m, 25)
m
vmf.mle(x)