A sequential procedure for estimating the mean of an exponential distribution is proposed. It is shown to perform well for large values of the mean, and the results of a Monte Carlo study indicate that it also performs well for moderate values of the mean.
Norman Starr. Michael Woodroofe. "Further Remarks on Sequential Estimation: The Exponential Case." Ann. Math. Statist. 43 (4) 1147 - 1154, August, 1972. https://doi.org/10.1214/aoms/1177692467