A truncated inverse binomial stopping rule can certify a mixed absolute-relative error bound for a probability estimate with a worst-case sample count near a quarter of the beta/alpha ratio times the Chernoff-Hoeffding count.
A theory of truncated inverse sampling,
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Probability Estimation with Truncated Inverse Binomial Sampling
A truncated inverse binomial stopping rule can certify a mixed absolute-relative error bound for a probability estimate with a worst-case sample count near a quarter of the beta/alpha ratio times the Chernoff-Hoeffding count.