largestRoot: Distribution of the largest root

Description Usage Arguments Details Value Examples

Description

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

Usage

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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

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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')

turgeonmaxime/rootWishart documentation built on June 1, 2019, 2:56 a.m.