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On the moment absolute deviation of order statistics from uniform distribution

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  • Kapelko, Rafał

Abstract

Assume that n mobile sensors with identical sensing range r=12n are distributed independently at random on the unit interval with the uniform distribution. We study the maximum sensor’s displacements to the power a>0 for full coverage of the unit interval in the sense that every point in the unit interval is within the range of a sensor. We derive the asymptotic result about the maximum of moments absolute deviation around the mean for order statistics from uniform distribution.

Suggested Citation

  • Kapelko, Rafał, 2022. "On the moment absolute deviation of order statistics from uniform distribution," Statistics & Probability Letters, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:stapro:v:181:y:2022:i:c:s0167715221002406
    DOI: 10.1016/j.spl.2021.109278
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    References listed on IDEAS

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    1. Doerr, Benjamin, 2018. "An elementary analysis of the probability that a binomial random variable exceeds its expectation," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 67-74.
    2. Eghbal, Negar, 2021. "Some inequalities for absolute moments of feasible acceptable random variables," Statistics & Probability Letters, Elsevier, vol. 172(C).
    3. Ushakov, N.G., 2011. "Some inequalities for absolute moments," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 2011-2015.
    4. Rafał Kapelko, 2018. "On the moment distance of Poisson processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(24), pages 6052-6063, December.
    5. Janson, Svante, 2021. "On the probability that a binomial variable is at most its expectation," Statistics & Probability Letters, Elsevier, vol. 171(C).
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