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In this letter, we present an improved hazard rate twisting technique for theestimation of the probability that a sum of independent but not necessarilyidentically distributed subexponential Random Variables (RVs) exceeds a giventhreshold. Instead of twisting all the components in the summation, we proposeto twist only the RVs which have the biggest impact on the right-tail of thesum distribution and keep the other RVs unchanged. A minmax approach isperformed to determine the optimal twisting parameter which leads to anasymptotic optimality criterion. Moreover, we show through some selectedsimulation results that our proposed approach results in a variance reductioncompared to the technique where all the components are twisted.

An Improved Hazard Rate Twisting Approach for the Statistic of the Sum of Subexponential Variates (Extended Version)