= Adjacent count tails in an exact Poisson confidence interval
{title2=$F_{\lambda_L}(s-1)=1-\alpha/2,\quad F_{\lambda_U}(s)=\alpha/2$}
For a count $s>0$ from a <Poisson distribution>, equal-tail inversion uses the inclusive upper-tail event $S\geq s$ for the lower endpoint and the inclusive lower-tail event $S\leq s$ for the upper endpoint. Their cumulative distribution indices differ by one, as displayed. If $s=0$, the lower endpoint is zero. For $n$ observations of mean $\mu$, apply this to their total of mean $\lambda=n\mu$ and divide endpoints by $n$. The construction has at least the nominal frequentist coverage; discreteness can make it conservative.
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