Random values simulation from a von Mises-Fisher distribution

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Description

It generates random vectors following the von Mises-Fisher distribution. The data can be spherical or hyper-spherical.

Usage

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rvmf(n, mu, k)

Arguments

n

The sample size.

mu

The mean direction.

k

The concentration parameter. If k = 0, random values from the spherical uniform will be drwan. Values from a multivariate normal distribution with zero mean vector and the identity matrix as the covariance matrix. Then each vector becomes a unit vector.

Details

It uses a rejection smapling as suggested by Andrew Wood (1994).

Value

A matrix with the simulated data.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>

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, rfb, rvonmises, rmixvmf

Examples

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

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