One-tailed Type I error rates for balanced two-category UniODA with a random ordered attribute

Directional (one-tailed) two-category univariable optimal discriminant analysis has proved highly useful for applications involving ordered attributes. An important criterion in the use of this analysis for a given application is the generalized Type I error rate associated with a given level of classification accuracy. The distribution of optima arising from this analysis performed for random data had been discovered earlier, but not proven. This article presents a formal mathematical proof of this theoretical distribution for balanced applications.