Wishart distribution

The function dwishart() computes the density of a Wishart distribution.

The function rwishart() samples from a Wishart distribution.

The functions with suffix _cpp perform no input checks, hence are faster.

Usage

dwishart_cpp(x, df, scale, log = FALSE, inv = FALSE)

rwishart_cpp(df, scale, inv = FALSE)

dwishart(x, df, scale, log = FALSE, inv = FALSE)

rwishart(df, scale, inv = FALSE)

Arguments

x

[matrix()]
A covariance matrix of dimension p.

df

[integer()]
The degrees of freedom greater of equal p.

scale

[matrix()]
The scale covariance matrix of dimension p.

log

[logical(1)]
Return the logarithm of the density value?

inv

[logical(1)]
Use this inverse Wishart distribution?

Value

For dwishart(): The density value.

For rwishart(): A matrix, the random draw.

See also

Other simulation helpers: Simulator, correlated_regressors(), ddirichlet_cpp(), dmixnorm_cpp(), dmvnorm_cpp(), dtnorm_cpp(), gaussian_tv(), simulate_markov_chain()

Examples

x <- diag(2)
df <- 6
scale <- matrix(c(1, -0.3, -0.3, 0.8), ncol = 2)

# compute density
dwishart(x = x, df = df, scale = scale)
#> [1] 0.002607893
dwishart(x = x, df = df, scale = scale, log = TRUE)
#> [1] -5.949213
dwishart(x = x, df = df, scale = scale, inv = TRUE)
#> [1] 0.0004824907

# sample
rwishart(df = df, scale = scale)
#>            [,1]       [,2]
#> [1,]  4.2342718 -0.0589546
#> [2,] -0.0589546  1.3524160
rwishart(df = df, scale = scale, inv = TRUE)
#>            [,1]       [,2]
#> [1,]  0.2437757 -0.1430196
#> [2,] -0.1430196  0.2256511

# expectation of Wishart is df * scale
n <- 100
replicate(n, rwishart(df = df, scale = scale), simplify = FALSE) |>
  Reduce(f = "+") / n
#>           [,1]      [,2]
#> [1,]  5.558206 -1.552689
#> [2,] -1.552689  4.803429
df * scale
#>      [,1] [,2]
#> [1,]  6.0 -1.8
#> [2,] -1.8  4.8

# expectation of inverse Wishart is scale / (df - p - 1)
n <- 100
replicate(n, rwishart(df = df, scale = scale, TRUE), simplify = FALSE) |>
  Reduce(f = "+") / n
#>             [,1]        [,2]
#> [1,]  0.38708182 -0.09145206
#> [2,] -0.09145206  0.25241685
scale / (df - 2 - 1)
#>            [,1]       [,2]
#> [1,]  0.3333333 -0.1000000
#> [2,] -0.1000000  0.2666667