{"title":"Monitoring a Poisson process subject to gradual changes in the arrival rates where the arrival rates are unknown","authors":"Marlo Brown","doi":"10.1080/07474946.2021.1940504","DOIUrl":null,"url":null,"abstract":"Abstract 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.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sequential Analysis-Design Methods and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07474946.2021.1940504","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract 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.
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