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

Author

Listed:
  • Agah Kozan

    (Ege University)

  • Burak Uyar

    (Van Yüzüncü Yıl University)

  • Halil Tanil

    (Ege University)

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.

Suggested Citation

  • Agah Kozan & Burak Uyar & Halil Tanil, 2024. "Exceedance statistics based on bottom- $$k$$ k -lists," Statistical Papers, Springer, vol. 65(8), pages 5239-5251, October.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:8:d:10.1007_s00362-024-01581-x
    DOI: 10.1007/s00362-024-01581-x
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    References listed on IDEAS

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    1. Ismihan Bairamov & Samuel Kotz, 2001. "On distributions of exceedances associated with order statistics and record values for arbitrary distributions," Statistical Papers, Springer, vol. 42(2), pages 171-185, April.
    2. Eryilmaz, Serkan & Gebizlioglu, Omer L. & Tank, Fatih, 2011. "Modeling of claim exceedances over random thresholds for related insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 496-500.
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