Table 1.

Formulations of uncertainty intervals of compared methods: MRT, Dube and Bhat. Φ: cumulative normal distribution function.

Method name	Formulation
MRT	$-log\left(\frac{1}{1+\frac{1}{n}{\left({\mathrm{\Phi }}^{-1}\left(1-\frac{\alpha }{2}\right)\right)}^2}\left(\frac{k}{n}+\frac{{\left({\mathrm{\Phi }}^{-1}\left(1-\frac{\alpha }{2}\right)\right)}^2}{2n}\pm {\mathrm{\Phi }}^{-1}\left(1-\frac{\alpha }{2}\right)\sqrt{\frac{k^2}{n}\left(1-\frac{k}{n}\right)+\frac{{\left({\mathrm{\Phi }}^{-1}\left(1-\frac{\alpha }{2}\right)\right)}^2}{4n^2}}\right)\right)$
Bhat	$\lambda \pm \sqrt{\frac{\frac{k}{n}}{n(1-\frac{k}{n})}}$
Dube	$-log\left(1-\frac{k}{n}\pm {\mathrm{\Phi }}^{-1}(1-\frac{\alpha }{2})\sqrt{\frac{\frac{k}{n}(1-\frac{k}{n})}{n}}\right)$