Angular central Gaussian random values simulation: Angular central Gaussian random values simulation
Description
Angular central Gaussian random values simulation.
Usage
racg(n, sigma)
Value
A matrix with the simulated data.
Arguments
n
The sample size, a numerical value.
sigma
The covariance matrix in \(R^d\).
Author
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
Details
The algorithm uses univariate normal random values and transforms them to multivariate via a spectral decomposition.
The vectors are then scaled to have unit length.
References
Tyler D. E. (1987). Statistical analysis for the angular central Gaussian distribution on the sphere. Biometrika 74(3): 579--589.
s <- cov( iris[, 1:4] )
x <- racg(100, s)
Directional::acg.mle(x)
Directional::vmf.mle(x)
## the concentration parameter, kappa, is very low, close to zero, as expected.