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The variance of the power of a shifted random variable with applications

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  • Budny, Katarzyna

Abstract

In the paper we analyze the variance of the power of a random variable. Moreover, using the variance of the power of a shifted random variable we present some improvement of the power generalization of Cantelli’s inequality for a positive random variable.

Suggested Citation

  • Budny, Katarzyna, 2022. "The variance of the power of a shifted random variable with applications," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s0167715221002753
    DOI: 10.1016/j.spl.2021.109317
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    References listed on IDEAS

    as
    1. Haruhiko Ogasawara, 2020. "Some Improvements on Markov's Theorem with Extensions," The American Statistician, Taylor & Francis Journals, vol. 74(3), pages 218-225, July.
    2. Katarzyna Budny, 2016. "An extension of the multivariate Chebyshev's inequality to a random vector with a singular covariance matrix," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(17), pages 5220-5223, September.
    3. Budny, Katarzyna, 2014. "A generalization of Chebyshev’s inequality for Hilbert-space-valued random elements," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 62-65.
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