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Given a stream of Bernoulli random variables, consider the problem ofestimating the mean of the random variable within a specified relative errorwith a specified probability of failure. Until now, the Gamma BernoulliApproximation Scheme (GBAS) was the method that accomplished this goal usingthe smallest number of average samples. In this work, a new method isintroduced that is faster when the mean is bounded away from zero. The processuses a two-stage process together with some simple inequalities to get rigorousbounds on the error probability.

Tight relative estimation in the mean of Bernoulli random variables