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

We look at a Poisson process where the arrival rates change from λ 1 to λ 2 . We will assume that the arrival rates both before and after the change are unknown. We also assume that this change does not happen abruptly but gradually over a period of time η where η is known. We calculate the probabil...

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Bibliographic Details
Published inSequential analysis Vol. 40; no. 3; pp. 427 - 440
Main Author Brown, Marlo
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.07.2021
Taylor & Francis Ltd
Subjects
Bayesian stopping rules
change-point detection
dynamic programming
False alarms
gradual changes
Poisson density functions
Poisson processes
Statistical analysis
unknown arrival rates
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Summary:We look at a Poisson process where the arrival rates change from λ 1 to λ 2 . We will assume that the arrival rates both before and after the change are unknown. We also assume that this change does not happen abruptly but 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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0747-4946
1532-4176
DOI:10.1080/07474946.2021.1940504