Some Distribution Problems Connected with the Characteristic Roots of $S_1S^{-1}_2$
Some Distribution Problems Connected with the Characteristic Roots of $S_1S^{-1}_2$
Let $\mathbf{S}_i : p \times p (i = 1,2)$ be independently distributed as Wishart $(n_i, p, \mathbf{\sigma}_i)$. Let the characteristic (ch) roots of $\mathbf{S}_1\mathbf{S}^{-1}_2$ and $\mathbf{\sigma}_1\mathbf{\sigma}^{-1}_2$ be denoted by $f_i (i = 1, 2,\cdots, p)$ and $\lambda_i(i = 1, 2, \cdots, p)$ respectively such that $0 < f_1 < f_2 …