Draw from Wishart distribution

This function draws from a Wishart and inverted Wishart distribution.

Usage

rwishart(nu, V)

Arguments

nu

A numeric, the degrees of freedom. Must be at least the number of dimensions.

V

A matrix, the scale matrix.

Value

A list, the draws from the Wishart (W), inverted Wishart (IW), and corresponding Choleski decomposition (C and CI).

Details

The Wishart distribution is a generalization to multiple dimensions of the gamma distributions and draws from the space of covariance matrices. Its expectation is nu*V and its variance increases both in nu and in the values of V. The Wishart distribution is the conjugate prior to the precision matrix of a multivariate normal distribution and proper if nu is greater than the number of dimensions.

Examples

rwishart(nu = 2, V = diag(2))
#> $W
#>           [,1]      [,2]
#> [1,]  1.277530 -2.393022
#> [2,] -2.393022  4.494557
#> 
#> $IW
#>          [,1]      [,2]
#> [1,] 292.2886 155.62223
#> [2,] 155.6222  83.07991
#> 
#> $C
#>          [,1]       [,2]
#> [1,] 1.130279 -2.1171964
#> [2,] 0.000000  0.1097115
#> 
#> $CI
#>           [,1]      [,2]
#> [1,] 0.8847376 17.073542
#> [2,] 0.0000000  9.114818
#>