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Noonan J, Zhigljavsky A. Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables. Methodol Comput Appl Probab 2020. [DOI: 10.1007/s11009-019-09769-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Abstract
AbstractIn 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.
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Noonan J, Zhigljavsky A. Approximations for the boundary crossing probabilities of moving sums of normal random variables. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2019.1626889] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Jack Noonan
- School of Mathematics, Cardiff University, Cardiff, UK
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Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data. Methodol Comput Appl Probab 2019. [DOI: 10.1007/s11009-018-9668-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Bin Hu, Seiler P. Probability bounds for false alarm analysis of fault detection systems. 2013 51ST ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON) 2013. [DOI: 10.1109/allerton.2013.6736633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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