Abstract
A general method for determining the exact null density and distribution of U ( p) , a constant times Hotelling's generalized T 0 2 statistic, for integral values of m ( = (n 1 − 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.
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