matrixsampling (version 2.0.0)

rmatrixbetaII: Matrix Beta II sampler

Description

Samples a matrix Beta type II distribution.

Usage

rmatrixbetaII(n, p, a, b, Theta1 = NULL, Theta2 = NULL, def = 1,
  checkSymmetry = TRUE)

Arguments

n

sample size, a positive integer

p

dimension, a positive integer

a, b

parameters of the distribution, positive numbers with constraints given in Details

Theta1

numerator noncentrality parameter, a positive semidefinite real matrix of order p; setting it to NULL (default) is equivalent to setting it to the zero matrix

Theta2

denominator noncentrality parameter, a positive semidefinite real matrix of order p; setting it to NULL (default) is equivalent to setting it to the zero matrix

def

1 or 2, the definition used; see Details

checkSymmetry

logical, whether to check the symmetry of Theta1 and Theta2

Value

A numeric three-dimensional array; simulations are stacked along the third dimension (see example).

Warning

The issue described in the Warning section of rmatrixbeta also concerns rmatrixbetaII.

Details

A Beta type II random matrix \(V\) is defined as follows. Take two independent Wishart random matrices

and .

• definition 1:

• definition 2:

In the central case, the two definitions yield the same distribution. Under definition 2, the Beta type II distribution is related to the Beta distribution by .

Parameters a and b are positive numbers that satisfy the following constraints:

• in any case, b > (p-1)/2

• if Theta1 is the null matrix and a < (p-1)/2, then a must be half an integer

• if Theta1 is not the null matrix, a >= (p-1)/2

Examples

# NOT RUN {
Bsims <- rmatrixbetaII(10000, 3, 1, 1.5)
dim(Bsims) # 3 3 10000
# }