#' Simulation from a Wishart distribution
#'
#' Simulates a random Wishart-distributed matrix
#'
#'
#' @usage rwish(S0, nu = dim(S0)[1] + 1)
#' @param S0 a positive definite matrix
#' @param nu a positive integer
#' @return a positive definite matrix
#' @author Peter Hoff
#' @examples
#'
#' ## The expectation is S0*nu
#'
#' S0<-rwish(diag(3))
#'
#' SS<-matrix(0,3,3)
#' for(s in 1:1000) { SS<-SS+rwish(S0,5) }
#'
#' SS/s
#'
#' S0*5
#'
#'
#' @export rwish
rwish <-
function(S0,nu=dim(S0)[1]+1)
{
# sample from a Wishart distribution
# with expected value nu*S0
sS0<-chol(S0)
Z<-matrix(rnorm(nu*dim(S0)[1]),nu,dim(S0)[1])%*%sS0
t(Z)%*%Z
}
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