nicheROVER (version 1.1.2)

rwish: Random draws from a Wishart (or Inverse-Wishart) distribution.

Description

Generates a random samples from a Wishart distribution defined as \(W(\Psi, \nu)\), or an Inverse-Wishart distribution defined as \(W^{-1}(\Psi, \nu)\).

Usage

rwish(n, Psi, nu, inv = FALSE)

Value

Returns an array of Wishart (or Inverse-Wishart) draws of size c(nrow(Psi),ncol(Psi),n).

Arguments

n

Number of samples to draw.

Psi

Scale matrix.

nu

Degrees of freedom.

inv

Logical. Setting inv = TRUE returns random matrices from an Inverse-Wishart distribution. See 'Details'.

Details

Setting inv = TRUE replaces \(\Psi\) by \(Psi^{-1}\) and inverts the output random matrices, such that they are being generated from an Inverse-Wishart \(W^{-1}(\Psi, \nu)\) distribution.

See Also

rniw()

Examples

d <- 4 # number of dimensions
nu <- 7 # degrees of freedom
Psi <- crossprod(matrix(rnorm(d^2), d, d)) # scale matrix
n <- 1e4

Sigma <- rwish(n, Psi, nu)

# for any vector a, X = (a' Sigma a) has a const * chi^2 distribution
a <- rnorm(d)
X <- apply(Sigma, 3, function(S) crossprod(a, S %*% a))
const <- c(a %*% Psi %*% a)

hist(X, breaks = 100, freq = FALSE,
     main = parse(text = "\"Histogram of \"*X==a*minute*Sigma*a"),
     xlab = parse(text = "X==a*minute*Sigma*a"))
curve(dchisq(x/const, df = nu)/const,
      from = min(X), to = max(X), col = "red", add = TRUE)