Simulation of random values from rotationally symmetric distributions
Simulation of random values from rotationally symmetric distributions. The data can be spherical or hyper-spherical.
rvmf(n, mu, k) riag(n, mu)
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. |
The von Mises-Fisher uses the rejection smapling suggested by Andrew 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.
A matrix with the simulated data.
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>
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
m <- rnorm(4) m <- m/sqrt(sum(m^2)) x <- rvmf(100, m, 25) m vmf.mle(x)
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