rInvWishart {CholWishart}

Random Inverse Wishart Distributed Matrices

Description

Generate n random matrices, distributed according to the inverse Wishart distribution with parameters Sigma and df, W_p(Sigma, df).

Note there are different ways of parameterizing the Inverse Wishart distribution, so check which one you need. Here, if X \sim IW_p(\Sigma, \nu) then X^{-1} \sim W_p(\Sigma^{-1}, \nu). Dawid (1981) has a different definition: if X \sim W_p(\Sigma^{-1}, \nu) and \nu > p - 1, then X^{-1} = Y \sim IW(\Sigma, \delta), where \delta = \nu - p + 1.

Usage

rInvWishart(n, df, Sigma)

Arguments

n

integer sample size.

df

numeric parameter, "degrees of freedom".

Sigma

positive definite p \times p "scale" matrix, the matrix parameter of the distribution.

Value

a numeric array, say R, of dimension p \times p \times n, where each R[,,i] is a realization of the inverse Wishart distribution IW_p(Sigma, df). Based on a modification of the existing code for the rWishart function.

References

Dawid, A. (1981). Some Matrix-Variate Distribution Theory: Notational Considerations and a Bayesian Application. Biometrika, 68(1), 265-274. doi: 10.2307/2335827

Gupta, A. K. and D. K. Nagar (1999). Matrix variate distributions. Chapman and Hall.

Mardia, K. V., J. T. Kent, and J. M. Bibby (1979) Multivariate Analysis, London: Academic Press.

See Also

rWishart, rCholWishart, and rInvCholWishart

Examples

set.seed(20180221)
A <- rInvWishart(1L, 10, 5 * diag(5L))[, , 1]
set.seed(20180221)
B <- stats::rWishart(1L, 10, .2 * diag(5L))[, , 1]

A %*% B