Ben Rached, N, Benkhelifa, F, Kammoun, A et al. (2 more authors) (2018) On the generalization of the hazard rate twisting-based simulation approach. Statistics and Computing, 28 (1). pp. 61-75. ISSN 0960-3174
Abstract
Estimating the probability that a sum of random variables (RVs) exceeds a given threshold is a well-known challenging problem. A naive Monte Carlo simulation is the standard technique for the estimation of this type of probability. However, this approach is computationally expensive, especially when dealing with rare events. An alternative approach is represented by the use of variance reduction techniques, known for their efficiency in requiring less computations for achieving the same accuracy requirement. Most of these methods have thus far been proposed to deal with specific settings under which the RVs belong to particular classes of distributions. In this paper, we propose a generalization of the well-known hazard rate twisting Importance Sampling-based approach that presents the advantage of being logarithmic efficient for arbitrary sums of RVs. The wide scope of applicability of the proposed method is mainly due to our particular way of selecting the twisting parameter. It is worth observing that this interesting feature is rarely satisfied by variance reduction algorithms whose performances were only proven under some restrictive assumptions. It comes along with a good efficiency, illustrated by some selected simulation results comparing the performance of the proposed method with some existing techniques.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Springer Science+Business Media New York 2016. This is an author produced version of article published in Statistics and Computing. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Naive Monte Carlo; Rare events; Importance sampling; Hazard rate twisting; Logarithmic efficient; Twisting parameter |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 30 Mar 2023 10:47 |
Last Modified: | 30 Mar 2023 10:47 |
Published Version: | http://dx.doi.org/10.1007/s11222-016-9716-4 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s11222-016-9716-4 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:195470 |