On the exact distribution of Hotelling's generalized T02

A general method for determining the exact null density and distribution of U(p), a constant times Hotelling's generalized statistic, for integral values of m ( = (n1 - p - 1)/2) is provided by inversion of Laplace transforms. The density of U(p) has been given explicitly for p = 3 and 4, and small values of m. Three approximations to the distribution of U(p) are also discussed and comparisons made with the exact distribution.