A System of Linear Differential Equations for the Distribution of Hotelling's Generalized $T_o^2$
A System of Linear Differential Equations for the Distribution of Hotelling's Generalized $T_o^2$
Let $\mathscr{S}_1, \mathscr{S}_2$ be independent $m \times m$ matrices on $n_1, n_2$ degrees of freedom respectively, $\mathscr{S}_2$ having a Wishart distribution and $\mathscr{S}_1$ having a possibly non-central Wishart distribution with the same covariance matrix. Hotelling's generalized $T_0^2$ statistic is then defined [7] by \begin{equation*}\tag{1.1}T = n^{-1}_2T_0^2 = \operatorname{tr} \mathscr{S}_1\mathscr{S}^{-1}_2.\end{equation*} The …