rFractionalWishart {rWishart}

Random Fractional Wishart Matrix

Description

Generate n random matrices, distributed according to the Wishart distribution with parameters Sigma and df, W_p(Sigma, df).

Usage

rFractionalWishart(n, df, Sigma, covariance = FALSE,
  simplify = "array")

Arguments

n

integer: the number of replications.

df

numeric parameter, “degrees of freedom”.

Sigma

positive definite (p\times p) “scale” matrix, the matrix parameter of the distribution.

covariance

logical on whether a covariance matrix should be generated

simplify

logical or character string; should the result be simplified to a vector, matrix or higher dimensional array if possible? For sapply it must be named and not abbreviated. The default value, TRUE, returns a vector or matrix if appropriate, whereas if simplify = "array" the result may be an array of “rank” (=length(dim(.))) one higher than the result of FUN(X[[i]]).

Details

If X_1, ..., X_m is a sample of m independent multivariate Gaussians with mean vector 0, and covariance matrix Sigma, the distribution of M = X'X is W_p(Sigma, m).

Value

A numeric array of dimension p * p * n, where each array is a positive semidefinite matrix, a realization of the Wishart distribution W_p(Sigma, df)

References

Adhikari, S. (2008). Wishart random matrices in probabilistic structural mechanics. Journal of engineering mechanics, 134(12), doi: 10.1061/(ASCE)0733-9399(2008)134:12(1029).

Examples

rFractionalWishart(2, 22.5, diag(1, 20))