On asymptotic properties of spacings

IF 1.2 4区数学 Q2 STATISTICS & PROBABILITY

Statistics Pub Date : 2023-09-03 DOI:10.1080/02331888.2023.2260037

Alexandre Berred, Alexei Stepanov

引用次数: 0

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).

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关于间隔的渐近性质

摘要在本文中，我们研究了基于连续分布函数的阶统计量的间隔。在本文的开头，我们给出了间隔的分布结果和一种根据其尾部对分布进行分类的方法。然后利用该方法得到了间隔的渐近结果。利用Borel-Cantelli引理的一些特殊版本，得到了它们的强极限结果。在论文的最后，我们给出了一些说明性的例子。关键词:序统计量;间距;限制结果;smsc2020 -数学科学分类系统:6062致谢作者非常感谢两位匿名审稿人的有趣评论和意见。第二作者的工作得到了俄罗斯联邦科学和高等教育部的支持(协议号:075-02-2021-1748)。披露声明作者未报告潜在的利益冲突。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics 数学-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

12 months

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.