Random Nonsingular Wishart Matrix

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

rNonsingularWishart(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]]).

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)

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).

Examples

rNonsingularWishart(2, 20, diag(1, 5))
#> , , 1
#> 
#>           [,1]      [,2]       [,3]       [,4]      [,5]
#> [1,] 15.374968  3.230006  2.8168006 -1.1836827 -2.108909
#> [2,]  3.230006 14.213374  2.5764396 -1.7046481 -2.649192
#> [3,]  2.816801  2.576440 17.3149711  0.5975208  4.092945
#> [4,] -1.183683 -1.704648  0.5975208 10.8716170  1.313598
#> [5,] -2.108909 -2.649192  4.0929451  1.3135976 16.620885
#> 
#> , , 2
#> 
#>           [,1]       [,2]      [,3]      [,4]       [,5]
#> [1,] 20.565613 -5.8468928 -2.525587 -4.363362 -4.3310172
#> [2,] -5.846893 26.4898886  2.224945  1.499786 -0.5019079
#> [3,] -2.525587  2.2249454 19.659257  4.501279  1.4150396
#> [4,] -4.363362  1.4997860  4.501279 19.020576 -1.3705010
#> [5,] -4.331017 -0.5019079  1.415040 -1.370501 14.3529960
#>