rCholWishart {CholWishart}

Cholesky Factor of Random Wishart Distributed Matrices

Description

Generate n random matrices, distributed according to the Cholesky factorization of a Wishart distribution with parameters Sigma and df, W_p(Sigma, df) (known as the Bartlett decomposition in the context of Wishart random matrices).

Usage

rCholWishart(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 Cholesky decomposition of a sample from the Wishart distribution W_p(Sigma, df). Based on a modification of the existing code for the rWishart function.

References

Anderson, T. W. (2003). An Introduction to Multivariate Statistical Analysis (3rd ed.). Hoboken, N. J.: Wiley Interscience.

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

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

See Also

rWishart, rInvCholWishart

Examples

# How it is parameterized:
set.seed(20180211)
A <- rCholWishart(1L, 10, 3 * diag(5L))[, , 1]
A
set.seed(20180211)
B <- rInvCholWishart(1L, 10, 1 / 3 * diag(5L))[, , 1]
B
crossprod(A) %*% crossprod(B)

set.seed(20180211)
C <- chol(stats::rWishart(1L, 10, 3 * diag(5L))[, , 1])
C