{"title":"Exceedance statistics based on bottom- $$k$$ -lists","authors":"Agah Kozan, Burak Uyar, Halil Tanil","doi":"10.1007/s00362-024-01581-x","DOIUrl":null,"url":null,"abstract":"<p>Similar to usual lower records, Bottom-<span>\\(k\\)</span>-lists (Kozan and Tanil, İstatistik J Turk Stat Assoc 13:73–79, 2013) have a wide range of practical applications in meteorology, hydrology, sports, etc. Also, exceedance statistics can be viewed as a close relative to tolerance limits—an important field of statistical science. In this study, an idea of combining these two important subjects together is studied and an exceedance statistic is defined based on bottom-<span>\\(k\\)</span>-lists in an independent and identically distributed (iid) continuous random sequence. Probability mass function (pmf) of a selected exceedance statistic is obtained. Also, an illustrative application of the exceedance statistic is given.</p>","PeriodicalId":51166,"journal":{"name":"Statistical Papers","volume":"41 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Papers","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00362-024-01581-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Similar to usual lower records, Bottom-\(k\)-lists (Kozan and Tanil, İstatistik J Turk Stat Assoc 13:73–79, 2013) have a wide range of practical applications in meteorology, hydrology, sports, etc. Also, exceedance statistics can be viewed as a close relative to tolerance limits—an important field of statistical science. In this study, an idea of combining these two important subjects together is studied and an exceedance statistic is defined based on bottom-\(k\)-lists in an independent and identically distributed (iid) continuous random sequence. Probability mass function (pmf) of a selected exceedance statistic is obtained. Also, an illustrative application of the exceedance statistic is given.
与通常的较低记录类似，Bottom-\(k\)-lists（Kozan 和 Tanil，İstatistik J Turk Stat Assoc 13:73-79，2013 年）在气象学、水文学、体育等领域有着广泛的实际应用。此外，超限统计也可视为与容限的近亲--容限是统计科学的一个重要领域。本研究将这两个重要课题结合在一起进行研究，并基于独立且同分布（iid）的连续随机序列中的底（k\ ）列表定义了超限统计量。得出了所选超标统计量的概率质量函数（pmf）。此外，还给出了超标统计量的示例应用。
期刊介绍：
The journal Statistical Papers addresses itself to all persons and organizations that have to deal with statistical methods in their own field of work. It attempts to provide a forum for the presentation and critical assessment of statistical methods, in particular for the discussion of their methodological foundations as well as their potential applications. Methods that have broad applications will be preferred. However, special attention is given to those statistical methods which are relevant to the economic and social sciences. In addition to original research papers, readers will find survey articles, short notes, reports on statistical software, problem section, and book reviews.
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