rmatrixCHkind1: Sampler of the matrix variate confluent hypergometric kind... In matrixsampling: Simulations of Matrix Variate Distributions

Description

Samples the matrix variate confluent hypergometric kind one distribution.

Usage

 ```1 2``` ```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

 ```1 2 3 4 5 6``` ```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)) ```

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