Description Usage Arguments Details Value Examples
Computes the cumulative distribution function of the largest root in the single and double Wishart setting.
1 2 3 | singleWishart(x, p, n, type, verbose = TRUE)
doubleWishart(x, p, n, m, type, verbose = TRUE)
|
x |
Vector of numeric values at which to compute the CDF. |
p, n, m |
Parameters of the single and double Wishart settings. See details. |
type |
Character string. Select |
verbose |
Logical. If |
If S follows a Wishart(p,n) distribution, e.g. if we can write
S = X^TX,
where X is an n x p matrix with i.i.d rows coming
from a p-variate standard normal, then singleWishart
gives the
distribution of the largest root of S (i.e. its largest eigenvalue.
As its name indicates, the double Wishart setting involves two Wishart variables:
let A and B be Wishart(p,m) and Wishart(p,n), respectively.
If A+B is invertible, then doubleWishart
gives the distribution of
the largest root of
(A+B)^-1B
. Alternatively, it gives the distribution of the largest root of the determinantal equation
det(B - θ(A+B))
.
Returns the value of the CDF at x
. An attribute also records
the type of precision use for the computation.
1 2 3 4 5 6 7 | x1 <- seq(0, 30, length.out = 50)
y1 <- singleWishart(x1, p = 5, n = 10)
plot(x1, y1, type = 'l')
x2 <- seq(0, 1, length.out = 50)
y2 <- doubleWishart(x2, p = 10, n = 10, m = 200)
plot(x2, y2, type = 'l')
|
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