{"title":"关于间隔的渐近性质","authors":"Alexandre Berred, Alexei Stepanov","doi":"10.1080/02331888.2023.2260037","DOIUrl":null,"url":null,"abstract":"AbstractIn this work, we investigate spacings based on order statistics obtained from continuous distribution functions. At the beginning of the paper, we present distributional results for spacings and a method of classification of distributions according to their tails. Then we use this method to derive asymptotic results for spacings. By applying some special versions of Borel–Cantelli lemma, we obtain their strong limit results. At the end of the paper, we present some illustrative examples.Keywords: Order statisticsspacingslimit resultsMSC2020-Mathematical Sciences Classification System: 6062 AcknowledgmentsThe authors are deeply indebted to the two anonymous Reviewers for their interesting comments and remarks. The work of the second author was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2021-1748).Disclosure statementNo potential conflict of interest was reported by the author(s).","PeriodicalId":54358,"journal":{"name":"Statistics","volume":"37 1","pages":"0"},"PeriodicalIF":1.2000,"publicationDate":"2023-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On asymptotic properties of spacings\",\"authors\":\"Alexandre Berred, Alexei Stepanov\",\"doi\":\"10.1080/02331888.2023.2260037\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"AbstractIn this work, we investigate spacings based on order statistics obtained from continuous distribution functions. At the beginning of the paper, we present distributional results for spacings and a method of classification of distributions according to their tails. Then we use this method to derive asymptotic results for spacings. By applying some special versions of Borel–Cantelli lemma, we obtain their strong limit results. At the end of the paper, we present some illustrative examples.Keywords: Order statisticsspacingslimit resultsMSC2020-Mathematical Sciences Classification System: 6062 AcknowledgmentsThe authors are deeply indebted to the two anonymous Reviewers for their interesting comments and remarks. The work of the second author was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2021-1748).Disclosure statementNo potential conflict of interest was reported by the author(s).\",\"PeriodicalId\":54358,\"journal\":{\"name\":\"Statistics\",\"volume\":\"37 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/02331888.2023.2260037\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/02331888.2023.2260037","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
AbstractIn this work, we investigate spacings based on order statistics obtained from continuous distribution functions. At the beginning of the paper, we present distributional results for spacings and a method of classification of distributions according to their tails. Then we use this method to derive asymptotic results for spacings. By applying some special versions of Borel–Cantelli lemma, we obtain their strong limit results. At the end of the paper, we present some illustrative examples.Keywords: Order statisticsspacingslimit resultsMSC2020-Mathematical Sciences Classification System: 6062 AcknowledgmentsThe authors are deeply indebted to the two anonymous Reviewers for their interesting comments and remarks. The work of the second author was supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2021-1748).Disclosure statementNo potential conflict of interest was reported by the author(s).
期刊介绍：
Statistics publishes papers developing and analysing new methods for any active field of statistics, motivated by real-life problems. Papers submitted for consideration should provide interesting and novel contributions to statistical theory and its applications with rigorous mathematical results and proofs. Moreover, numerical simulations and application to real data sets can improve the quality of papers, and should be included where appropriate. Statistics does not publish papers which represent mere application of existing procedures to case studies, and papers are required to contain methodological or theoretical innovation. Topics of interest include, for example, nonparametric statistics, time series, analysis of topological or functional data. Furthermore the journal also welcomes submissions in the field of theoretical econometrics and its links to mathematical statistics.
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