Some results concerning the distributions of the actual error rates in linear discriminant analysis, under various assumptions about the parameters, are discussed. To determine the form in the one-variable case, formulas for the exact distribution and density functions of the actual error rates are presented. Formulas for the asymptotic distribution and asymptotic moments of the actual error rates in both the univariate and multivariate cases are also given.
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James Sayre (1980) studied this question.
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