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Is there a "nice" closed-from expression for the confidence interval (CI) of the reciprocal binomial proportion, $\frac{1}{p}$?

I'm actually looking for a CI for $\frac{N}{p}$, which will be a simple task once a CI for $\frac{1}{p}$ is in hand.

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  • $\begingroup$ I see now that the answer is "no", since if $a > b$, then $1/a < 1/b$. $\endgroup$ – compbiostats Jan 10 '19 at 21:27
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    $\begingroup$ I don't see how that would cause a problem; a probability statement about a parameter being between two bounds will translate into a similar statement about the transformed parameter, when the transformation is monotonic; the fact that the bounds "flip over" (upper bound moves to a lower bound and vice versa) when you take the reciprocal doesn't alter the fact that the new bounds will include the inverted parameter with the required probabilities. The biggest issue that will arise is that the interval for $p$ may include 0. $\endgroup$ – Glen_b Jan 11 '19 at 0:41