{"title":"拟合泊松过程的对数线性速率","authors":"C. Vallarino","doi":"10.1109/ARMS.1989.49612","DOIUrl":null,"url":null,"abstract":"Given a sample of repairable systems, the author models its failure behavior. Each system is assumed to be an independent realization of a nonhomogeneous Poisson process with underlying log-linear intensity function. The author finds the maximum-likelihood estimates of the unknown parameters, presenting the likelihood function and its derivatives. Accurate starting values are obtained through a graphical method for the case of an increasing intensity. Finally, a set of real data is borrowed from R.E. Barlow and B. Davis (1978) to illustrate the techniques.<<ETX>>","PeriodicalId":430861,"journal":{"name":"Proceedings., Annual Reliability and Maintainability Symposium","volume":"211 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Fitting the log-linear rate to Poisson processes\",\"authors\":\"C. Vallarino\",\"doi\":\"10.1109/ARMS.1989.49612\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a sample of repairable systems, the author models its failure behavior. Each system is assumed to be an independent realization of a nonhomogeneous Poisson process with underlying log-linear intensity function. The author finds the maximum-likelihood estimates of the unknown parameters, presenting the likelihood function and its derivatives. Accurate starting values are obtained through a graphical method for the case of an increasing intensity. Finally, a set of real data is borrowed from R.E. Barlow and B. Davis (1978) to illustrate the techniques.<<ETX>>\",\"PeriodicalId\":430861,\"journal\":{\"name\":\"Proceedings., Annual Reliability and Maintainability Symposium\",\"volume\":\"211 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-01-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings., Annual Reliability and Maintainability Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARMS.1989.49612\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings., Annual Reliability and Maintainability Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARMS.1989.49612","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Given a sample of repairable systems, the author models its failure behavior. Each system is assumed to be an independent realization of a nonhomogeneous Poisson process with underlying log-linear intensity function. The author finds the maximum-likelihood estimates of the unknown parameters, presenting the likelihood function and its derivatives. Accurate starting values are obtained through a graphical method for the case of an increasing intensity. Finally, a set of real data is borrowed from R.E. Barlow and B. Davis (1978) to illustrate the techniques.<>
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