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A lower bound on the probability that a binomial random variable is exceeding its mean

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  • Pelekis, Christos
  • Ramon, Jan

Abstract

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.

Suggested Citation

  • Pelekis, Christos & Ramon, Jan, 2016. "A lower bound on the probability that a binomial random variable is exceeding its mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 305-309.
    • Handle: RePEc:eee:stapro:v:119:y:2016:i:c:p:305-309
    DOI: 10.1016/j.spl.2016.08.016
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    References listed on IDEAS

    as
    1. Berend, Daniel & Kontorovich, Aryeh, 2013. "A sharp estimate of the binomial mean absolute deviation with applications," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1254-1259.
    2. Greenberg, Spencer & Mohri, Mehryar, 2014. "Tight lower bound on the probability of a binomial exceeding its expectation," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 91-98.
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    Cited by:

    1. Li, Fu-Bo & Xu, Kun & Hu, Ze-Chun, 2023. "A study on the Poisson, geometric and Pascal distributions motivated by Chvátal’s conjecture," Statistics & Probability Letters, Elsevier, vol. 200(C).
    2. Idir Arab & Paulo Eduardo Oliveira & Tilo Wiklund, 2021. "Convex transform order of Beta distributions with some consequences," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 238-256, August.
    3. Barabesi, Lucio & Pratelli, Luca & Rigo, Pietro, 2023. "On the Chvátal–Janson conjecture," Statistics & Probability Letters, Elsevier, vol. 194(C).
    4. 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.
    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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