Random draws from a Wishart (or Inverse-Wishart) distribution.
Generates a random samples from a Wishart distribution defined as W(Ψ, ν), or an Inverse-Wishart distribution defined as W^{-1}(Ψ, ν).
rwish(n, Psi, nu, inv = FALSE)
n |
number of samples to draw. |
Psi |
scale matrix. |
nu |
degrees of freedom. |
inv |
logical. Setting |
Setting inv = TRUE replaces Ψ by Psi^{-1} and inverts the output random matrices,
such that they are being generated from an Inverse-Wishart W^{-1}(Ψ, ν) distribution.
Returns an array of Wishart (or Inverse-Wishart) draws of size c(nrow(Psi),ncol(Psi),n).
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 <- 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.