| rwishart {dlm} | R Documentation |
Random Wishart matrix
Description
Generate a draw from a Wishart distribution.
Usage
rwishart(df, p = nrow(SqrtSigma), Sigma, SqrtSigma = diag(p))
Arguments
df |
degrees of freedom. It has to be integer. |
p |
dimension of the matrix to simulate. |
Sigma |
the matrix parameter Sigma of the Wishart distribution. |
SqrtSigma |
a square root of the matrix parameter Sigma of the
Wishart distribution. Sigma must be equal to |
Details
The Wishart is a distribution on the set of nonnegative definite symmetric matrices. Its density is
p(W) = \frac{c |W|^{(n-p-1)/2}}{|\Sigma|^{n/2}}
\exp\left\{-\frac{1}{2}\mathrm{tr}(\Sigma^{-1}W)\right\}
where n is the degrees of freedom parameter df and
c is a normalizing constant.
The mean of the Wishart distribution is n\Sigma and the
variance of an entry is
\mathrm{Var}(W_{ij}) = n (\Sigma_{ij}^2 +
\Sigma_{ii}\Sigma_{jj})
The matrix parameter, which should be a positive definite symmetric matrix, can be specified via either the argument Sigma or SqrtSigma. If Sigma is specified, then SqrtSigma is ignored. No checks are made for symmetry and positive definiteness of Sigma.
Value
The function returns one draw from the Wishart distribution with
df degrees of freedom and matrix parameter Sigma or
crossprod(SqrtSigma)
Warning
The function only works for an integer number of degrees of freedom.
Note
From a suggestion by B.Venables, posted on S-news
Author(s)
Giovanni Petris GPetris@uark.edu
References
Press (1982). Applied multivariate analysis.
Examples
rwishart(25, p = 3)
a <- matrix(rnorm(9), 3)
rwishart(30, SqrtSigma = a)
b <- crossprod(a)
rwishart(30, Sigma = b)