= Extreme-order-statistic tolerance interval
{title2=$n\approx\vartheta/\varepsilon,\quad(1+\vartheta)e^{-\vartheta}=\delta$}
The sample minimum and maximum enclose random population content given by the <uniformized sample range>. The exact failure probability for content at least $1-\varepsilon$ is $(1-\varepsilon)^{n-1}[1+(n-1)\varepsilon]$. For small $\varepsilon$, setting $n\varepsilon\approx\vartheta$ gives the displayed sample-size approximation at confidence $1-\delta$. The positive solution is unique for $0<\delta<1$, since $(1+\vartheta)e^{-\vartheta}$ decreases from one to zero. A tolerance interval concerns population content, rather than a <confidence interval> for a fixed parameter; the exact inequality should select the final integer size.
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