Errors on ratios of small numbers of events

Testing minimal lepton flavor violation with extra vectorlike leptons at the LHC

“…In such a case, the exact confidence intervals at a confidence level 1 À are given by the following formula [30]: shown in Figs. 7 and 8.…”

Techniques and Concepts of High-Energy Physics II

“…Later it was recognized that these values are in fact just those of Fisher's F-distribution with appropriately transformed ar-l'ofF===r========~~~;;:::===n guments, so that existing tables or subroutines of F can be used to determine exact confidence intervals for p. Additional details concerning this problem and the way in which it arises in the context of physics experiments, may be found in James and Roos (1980).…”

Treatment of Nuisance Parameters in High Energy Physics, and Possible Justifications and Improvements in the Statistics Literature

“…5, and found that they not only typically over-covered (as do confidence intervals for a Poisson mean), but that they always over-covered by a finite amount! There were no combinations of µ and ν for which the set of confidence intervals had coverage even close to the nominal confidence level.…”