Monitoring a Poisson process subject to gradual changes in the arrival rates

We look at a Poisson process where the arrival rates change from a known λ 1 to a known λ 2 . Whereas in most of the literature the change-point is abrupt, we model the more realistic assumption that states that the change happens gradually over a period of time η where η is known. We calculate the...

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Bibliographic Details
Published inSequential analysis Vol. 38; no. 3; pp. 358 - 368
Main Author Brown, Marlo
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.07.2019
Taylor & Francis Ltd
Subjects
Bayesian stopping rules
change-point detection
dynamic programming
False alarms
gradual changes
Poisson density functions
poisson processes
Random walk theory
Statistical analysis
Online AccessGet full text
ISSN0747-4946
1532-4176
DOI10.1080/07474946.2019.1648923

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Summary:We look at a Poisson process where the arrival rates change from a known λ 1 to a known λ 2 . Whereas in most of the literature the change-point is abrupt, we model the more realistic assumption that states that the change happens gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early. We conclude with some numerical results.
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ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2019.1648923