Ben Rached, N., Hoel, H. and Vincent Meo, J.V. (2024) A fast and accurate numerical method for the left tail of sums of independent random variables. Statistics and computing, 34. 202. ISSN 0960-3174
Abstract
We present a flexible, deterministic numerical method for computing left-tail rare events of sums of non-negative, independent random variables. The method is based on iterative numerical integration of linear convolutions by means of Newtons–Cotes rules. The periodicity properties of convoluted densities combined with the Trapezoidal rule are exploited to produce a robust and efficient method, and the method is flexible in the sense that it can be applied to all kinds of non-negative continuous RVs. We present an error analysis and study the benefits of utilizing Newton–Cotes rules versus the fast Fourier transform (FFT) for numerical integration, showing that although there can be efficiency benefits to using FFT, Newton–Cotes rules tend to preserve the relative error better, and indeed do so at an acceptable computational cost. Numerical studies on problems with both known and unknown rare-event probabilities showcase the method’s performance and support our theoretical findings.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Rare events; Discrete convolution; Newton–Cotes rule; FFT |
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: | 22 Oct 2024 11:12 |
Last Modified: | 22 Oct 2024 11:12 |
Status: | Published |
Publisher: | Springer Nature |
Identification Number: | 10.1007/s11222-024-10514-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:218667 |