# largestRoot: Distribution of the largest root In turgeonmaxime/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

 ```1 2 3``` ```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

 ```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') ```

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