{"title":"随机时间下检验悖论的量化","authors":"Diana Rauwolf, U. Kamps","doi":"10.1080/00031305.2022.2151510","DOIUrl":null,"url":null,"abstract":"Abstract The well-known inspection paradox of renewal theory states that, in expectation, the inspection interval is larger than a common renewal interval, in general. For a random inspection time, which includes the deterministic case, and a delayed renewal process, representations of the expected length of an inspection interval and related inequalities in terms of covariances are shown. Datasets of eruption times of Beehive Geyser and Riverside Geyser in Yellowstone National Park, as well as several distributional examples, illustrate the findings.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantifying the Inspection Paradox with Random Time\",\"authors\":\"Diana Rauwolf, U. Kamps\",\"doi\":\"10.1080/00031305.2022.2151510\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The well-known inspection paradox of renewal theory states that, in expectation, the inspection interval is larger than a common renewal interval, in general. For a random inspection time, which includes the deterministic case, and a delayed renewal process, representations of the expected length of an inspection interval and related inequalities in terms of covariances are shown. Datasets of eruption times of Beehive Geyser and Riverside Geyser in Yellowstone National Park, as well as several distributional examples, illustrate the findings.\",\"PeriodicalId\":342642,\"journal\":{\"name\":\"The American Statistician\",\"volume\":\"44 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The American Statistician\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00031305.2022.2151510\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The American Statistician","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00031305.2022.2151510","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantifying the Inspection Paradox with Random Time
Abstract The well-known inspection paradox of renewal theory states that, in expectation, the inspection interval is larger than a common renewal interval, in general. For a random inspection time, which includes the deterministic case, and a delayed renewal process, representations of the expected length of an inspection interval and related inequalities in terms of covariances are shown. Datasets of eruption times of Beehive Geyser and Riverside Geyser in Yellowstone National Park, as well as several distributional examples, illustrate the findings.
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