{"title":"更新过程中前向和后向递推时间的分布和矩的边界","authors":"Stathis Chadjiconstantinidis, Konstadinos Politis","doi":"10.1016/j.cam.2024.116166","DOIUrl":null,"url":null,"abstract":"<div><p>We obtain a variety of lower and upper bounds for the bivariate tail of the joint distribution between the (forward and backward) recurrence times in a renewal process. Some of these bounds are valid generally, some others in the case where the interarrival distribution <span><math><mi>F</mi></math></span> exhibits monotone aging. We also give various bounds for the moments of the recurrence times. Our results improve upon existing bounds for these quantities in the literature. We also discuss the case where the aging of <span><math><mi>F</mi></math></span> is non-monotonic. Finally, we present numerical examples to illustrate the performance of the new bounds.</p></div>","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bounds for the distribution and moments of the forward and backward recurrence times in a renewal process\",\"authors\":\"Stathis Chadjiconstantinidis, Konstadinos Politis\",\"doi\":\"10.1016/j.cam.2024.116166\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We obtain a variety of lower and upper bounds for the bivariate tail of the joint distribution between the (forward and backward) recurrence times in a renewal process. Some of these bounds are valid generally, some others in the case where the interarrival distribution <span><math><mi>F</mi></math></span> exhibits monotone aging. We also give various bounds for the moments of the recurrence times. Our results improve upon existing bounds for these quantities in the literature. We also discuss the case where the aging of <span><math><mi>F</mi></math></span> is non-monotonic. Finally, we present numerical examples to illustrate the performance of the new bounds.</p></div>\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0377042724004151\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724004151","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 0
摘要
我们得到了更新过程中（前向和后向）递归时间联合分布的双变量尾部的各种下限和上限。其中一些边界在一般情况下有效，另一些则在到达间分布 F 呈现单调老化的情况下有效。我们还给出了递推时间矩的各种约束。我们的结果改进了文献中对这些量的现有约束。我们还讨论了 F 的老化是非单调的情况。最后，我们通过数字示例来说明新边界的性能。
Bounds for the distribution and moments of the forward and backward recurrence times in a renewal process
We obtain a variety of lower and upper bounds for the bivariate tail of the joint distribution between the (forward and backward) recurrence times in a renewal process. Some of these bounds are valid generally, some others in the case where the interarrival distribution exhibits monotone aging. We also give various bounds for the moments of the recurrence times. Our results improve upon existing bounds for these quantities in the literature. We also discuss the case where the aging of is non-monotonic. Finally, we present numerical examples to illustrate the performance of the new bounds.
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