rmatrixCHkind1 {matrixsampling}

Sampler of the matrix variate confluent hypergometric kind one distribution

Description

Samples the matrix variate confluent hypergometric kind one distribution.

Usage

rmatrixCHkind1(n, nu, alpha, beta, theta = 1, 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

alpha, beta

shape parameters with the following constraints: b = a or b > a > nu + (p-1)/2

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

Value

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

Note

For alpha = beta, this is the matrix variate Gamma distribution with parameters nu, theta, Sigma.

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 <- 5; alpha <- 10; beta <- 12; theta <- 2; p <- 3; Sigma <- toeplitz(3:1)
CHsims <- rmatrixCHkind1(10000, nu, alpha, beta, theta, Sigma)
# simulations of the trace
sims <- apply(CHsims, 3, function(X) sum(diag(X)))
mean(sims)
theta * nu * (nu-beta+(p+1)/2) / (nu-alpha+(p+1)/2) * sum(diag(Sigma))