Abstract
SUMMARY This paper demonstrates that for a rich class of problems the distribution of internally studentized statistics can be obtained from the distribution of the corresponding unstudentized statistics via an inverse Laplace transform. Various known results are easily rederived or extended by use of this theorem; among these are results for problems involving random divisions of an interval, residual analysis, ratios of quadratic forms in normal variables, and latent roots of a central Wishart matrix.
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