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What would be the analog of the "rule of three", but for a 99% confidence interval?

I.e., how to estimate, with the 99% confidence, the rate of occurrences in the population after looking at a sample with n subjects which didn't have the given event occurring?

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  • $\begingroup$ The rule of three is for a situation where the outcome is an event that happens or not (not measured variable) and the event did not occur in the n observations. If you are asking for the corresponding value for 99% CI, please add those details to your question. $\endgroup$ Commented Jan 2 at 15:55
  • $\begingroup$ I've added the detail that the given event didn't happen in the given sample. Thanks. $\endgroup$ Commented Jan 2 at 15:58
  • $\begingroup$ Search for "Rule of Three" log. $\endgroup$ Commented Jan 2 at 16:08
  • $\begingroup$ The links give an overwhelming number of different formulas, but for posterity stats.stackexchange.com/a/34102/455846 says the answer is the "rule of 4.6". $\endgroup$ Commented Jan 2 at 16:19
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    $\begingroup$ You might find it more useful to refer to this as the "Rule of $-log(\alpha).$" For 95% confidence, alpha = 5% while for 99% confidence alpha = 1%. It is a short step from that to remembering the underlying principle, as discussed in any of the derivations, which is simply the definition of a confidence limit. $\endgroup$ Commented Jan 2 at 16:45

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