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This paper presents the asymptotic distributions of a generallikelihood-based test statistic, derived using results of Wilks and Wald. Thegeneral form of the test statistic incorporates the test statistics andassociated asymptotic formulae previously derived by Cowan, Cranmer, Gross andVitells, which are seen to be special cases of the likelihood-based teststatistic described here.

Asymptotic Formula for a General Double-Bounded Custom-Sided Likelihood Based Test Statistic