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Approximations for the boundary crossing probabilities of moving sums of random variables

Noonan, Jack and Zhigljavsky, Anatoly 2021. Approximations for the boundary crossing probabilities of moving sums of random variables. Methodology and Computing in Applied Probability 23 , pp. 873-892. 10.1007/s11009-019-09769-7

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Abstract

In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal random variables. We approximate a discrete time problem with a continuous time problem allowing us to apply established theory for stationary Gaussian processes. By then subsequently correcting approximations for discrete time, we show that the developed approximations are very accurate even for a small window length. Also, they have high accuracy when the original r.v. are not exactly normal and when the weights in the moving window are not all equal. We then provide accurate and simple approximations for ARL, the average run length until crossing the boundary.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher: Springer Verlag (Germany)
ISSN: 1387-5841
Date of First Compliant Deposit: 2 July 2020
Date of Acceptance: 26 December 2019
Last Modified: 11 Oct 2021 14:04
URI: http://orca.cardiff.ac.uk/id/eprint/131528

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