Simulation of random values from a spherical Kent distribution: Simulation of random values from a spherical Kent distribution
Description
Simulation of random values from a spherical Kent distribution.
Usage
rkent(n, k, m, b)
Value
A matrix with the simulated data.
Arguments
n
The sample size.
k
The concentraion parameter \(\kappa\). It has to be greater than 0.
m
The mean direction (Fisher part).
b
The ovalness parameter, \(\beta\).
Author
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
Details
Random values from a Kent distribution on the sphere are generated. The function generates from a spherical Kent distribution using rfb with an arbitrary mean direction and then rotates the data to have the desired mean direction.
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
k <- 15
mu <- rnorm(3)
mu <- mu / sqrt( sum(mu^2) )
A <- diag( c(-5, 0, 5) )
x <- rfb(500, k, mu, A)
kent.mle(x)
y <- rkent(500, k, mu, A[3, 3])
kent.mle(y)