Sample from the distribution of eigenvalues of W * inv(T)

Samples from the rp-dimensional joint distribution of the eigenvalues of \(WT^{-1}\), where \(W\) and \(T\) are independent Wisharts with dimensions specified in Prop 1(ii). These are the \(\Psi_i\), and taking \(\sqrt{(\Psi_i/(1+\Psi_i))}\) gives a sample from the joint distribution of the canonical correlations between two groups of variables of size \(p_1\) and \(p_2\) under the null.

Usage

sample_psi(p, rp, n)

Arguments

p

\(p_1+p_2\)

rp

\(min(p_1, p_2)\)

n

sample size

Value

A vector of length rp sampled from the joint distribution described above.