Exceedance statistics based on bottom- $$k$$ k -lists

Agah Kozan (), Burak Uyar and Halil Tanil
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Agah Kozan: Ege University
Burak Uyar: Van Yüzüncü Yıl University
Halil Tanil: Ege University

Statistical Papers, 2024, vol. 65, issue 8, No 17, 5239-5251

Abstract: Abstract Similar to usual lower records, Bottom- $$k$$ 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- $$k$$ 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.

Keywords: Exceedance statistics; Bottom- $$k$$ k -lists; Order statistics; Record values; Hypothesis testing; 60E05; 62E15; 62G10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-024-01581-x

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