Wishart distribution

Density and random generation for the wishart distribution

Usage

dwishart(x, nu, Sigma, log = FALSE)

rwishart(n, nu, Sigma)

Arguments

x

positive definite \(p \times p\) matrix or array of such matrices of dimension \(p \times p \times n\) (for \(n\) density evaluations)

nu

degrees of freedom, needs to be greater than p - 1

Sigma

scale matrix, needs to be positive definite and match the dimension of x.

log

logical; if TRUE, densities \(p\) are returned as \(\log(p)\).

n

number of random deviates to return

Value

dwishart gives the density, rwishart generates random deviates (matrix for n = 1, array with n slices for n > 1)

Examples

# single input: matrix-valued
x <- rwishart(1, nu = 5, Sigma = diag(3))
d <- dwishart(x, nu = 5, Sigma = diag(3))

# multiple inputs: array of matrices
x <- rwishart(4, nu = 5, Sigma = diag(3))
d <- dwishart(x, nu = 5, Sigma = diag(3))

# multiple inputs for x, nu and Sigma
nu <- c(7,5,8,9)
Sigma <- array(dim = c(3,3,4))
for(i in 1:4) Sigma[,,i] <- (i + 3) * diag(3)
x <- rwishart(4, nu, Sigma)
d <- dwishart(x, nu, Sigma)