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Let  ,...,  be i.i.d. subexponential and   =   + ⋯ +  . Asmussen and Kroese (Adv Appl Probab 38:545–558, ) suggested a simulation estimator for evaluating , combining an exchangeability argument with conditional Monte Carlo. The estimator was later shown by Hartinger and Kortschak (Bl DGVFM 30:363–377, ) to have vanishing relative error. For the Weibull and related cases, we calculate the exact error rate and suggest improved estimators. These improvements can be seen as control variate estimators, but are rather motivated by second order subexponential theory which is also at the core of the technical proofs.

Error Rates and Improved Algorithms for Rare Event Simulation with Heavy Weibull Tails