largestRoot: Distribution of the largest root

In rootWishart: Distribution of Largest Root for Single and Double Wishart Settings

Description

Computes the cumulative distribution function of the largest root in the single and double Wishart setting.

Usage

singleWishart(x, p, n, type = c("double", "multiple"))

doubleWishart(x, p, n, m, type = c("double", "multiple"))

Arguments

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 type = "multi" for multiprecision; select type = "double" for double precision. Defaults to adaptive selection of the precision type based on the input parameters.

Details

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.

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 determinental equation

det(B - θ(A+B)).

Value

Returns the value of the CDF at x.

Examples

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')

rootWishart documentation built on May 2, 2019, 3:42 p.m.