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Conference Papers Year : 2023

Bounds, Assessment and Confidence Intervals for Exponential Approximations


Geometric sums can often be approximated by an exponential random variable when the number of summands is large, simplifying estimations in many rare contexts. It is typically the case when estimating the distribution of the waiting time in an M/G/1 queue or the hitting time to a rare set for a regenerative process. One of the main advantages of the approximation is to reduce the estimation of the whole distribution to the estimation of its mean, for which efficient (rare event) simulation are usually available in the literature. Though, the approximation error introduces a bias to the estimation which needs to be assessed and ensured to be negligible with respect to the statistical error, or included in the overall estimation error. This presentation contributes to solve this issue: it provides deterministic approximation bounds when parameters are known, which can be used to control the validity of the estimation and to propose thresholds on the mean of the geometric number of summands for which the approximation is advised to be used.
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hal-04215951 , version 1 (23-09-2023)




  • HAL Id : hal-04215951 , version 1


Peter W Glynn, Marvin K Nakayama, Bruno Tuffin. Bounds, Assessment and Confidence Intervals for Exponential Approximations. MCM 2023 - 14th International Conference on Monte Carlo Methods, Jun 2023, Paris, France. pp.1. ⟨hal-04215951⟩
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