rmatrixgamma: Matrix Gamma sampler

In matrixsampling: Simulations of Matrix Variate Distributions

Description

Samples a matrix Gamma distribution.

Usage

rmatrixgamma(n, nu, theta, Sigma = NULL, p, checkSymmetry = TRUE)

Arguments

n	sample size, a positive integer
nu	shape parameter, a positive number; if nu < (p-1)/2, where p is the dimension (the order of Sigma), then nu must be a half integer
theta	scale parameter, a positive number
Sigma	scale matrix, a symmetric positive definite matrix, or NULL for the identity matrix of order p
p	if Sigma is NULL, this sets Sigma to the identity matrix of order p; ignored if Sigma is not NULL
checkSymmetry	logical, whether to check that Sigma is a symmetric positive definite matrix

Details

This is the distribution of θ/2×S where S ~ W_p(2ν,Σ).

Value

A numeric three-dimensional array; simulations are stacked along the third dimension.

References

Gupta & al. Properties of Matrix Variate Confluent Hypergeometric Function Distribution. Journal of Probability and Statistics vol. 2016, Article ID 2374907, 12 pages, 2016.

Examples

nu <- 3; theta <- 4; Sigma <- toeplitz(2:1)
Gsims <- rmatrixgamma(10000, nu, theta, Sigma)
apply(Gsims, c(1,2), mean) # should be nu * theta * Sigma
nu * theta * Sigma

Example output

         [,1]     [,2]
[1,] 23.79843 11.85630
[2,] 11.85630 23.86054
     [,1] [,2]
[1,]   24   12
[2,]   12   24

matrixsampling documentation built on Aug. 25, 2019, 1:03 a.m.