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(n = 1, df, scale, inv = FALSE)Arguments
- x
[
matrix()]
A covariance matrix of dimensionp.- df
[
numeric(1)]
The degrees of freedom, at leastp.- scale
[
matrix()]
The scale covariance matrix of dimensionp.- log
[
logical(1)]
Return the logarithm of the density value?- inv
[
logical(1)]
Use this inverse Wishart distribution?- n
[
integer(1)]
The number of requested samples.
Value
For dwishart(): The density value.
For rwishart(): If n = 1 a matrix of dimension p times p, else
an array of dimension p times p times n with the draws as slices.
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,] 10.916213 -3.044349
#> [2,] -3.044349 6.055640
rwishart(df = df, scale = scale, inv = TRUE)
#> [,1] [,2]
#> [1,] 0.6896157 -0.1497311
#> [2,] -0.1497311 0.1339354
# expectation of Wishart is df * scale
apply(rwishart(n = 100, df = df, scale = scale), 1:2, mean)
#> [,1] [,2]
#> [1,] 5.450034 -1.778992
#> [2,] -1.778992 4.881211
df * scale
#> [,1] [,2]
#> [1,] 6.0 -1.8
#> [2,] -1.8 4.8
# expectation of inverse Wishart is scale / (df - p - 1)
apply(rwishart(n = 100, df = df, scale = scale, inv = TRUE), 1:2, mean)
#> [,1] [,2]
#> [1,] 0.39347712 -0.09653709
#> [2,] -0.09653709 0.25599598
scale / (df - 2 - 1)
#> [,1] [,2]
#> [1,] 0.3333333 -0.1000000
#> [2,] -0.1000000 0.2666667