IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v86y2014icp91-98.html
   My bibliography  Save this article

Tight lower bound on the probability of a binomial exceeding its expectation

Author

Listed:
  • Greenberg, Spencer
  • Mohri, Mehryar

Abstract

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded loss functions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:86:y:2014:i:c:p:91-98
    DOI: 10.1016/j.spl.2013.12.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715213004082
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2013.12.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lesch, Scott M. & Jeske, Daniel R., 2009. "Some Suggestions for Teaching About Normal Approximations to Poisson and Binomial Distribution Functions," The American Statistician, American Statistical Association, vol. 63(3), pages 274-277.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Narayanaswamy Balakrishnan & Efe A. Ok & Pietro Ortoleva, 2021. "Inferential Choice Theory," Working Papers 2021-60, Princeton University. Economics Department..
    2. 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).
    3. 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.
    4. 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.
    5. Barabesi, Lucio & Pratelli, Luca & Rigo, Pietro, 2023. "On the Chvátal–Janson conjecture," Statistics & Probability Letters, Elsevier, vol. 194(C).
    6. Pinelis, Iosif, 2021. "Best lower bound on the probability of a binomial exceeding its expectation," Statistics & Probability Letters, Elsevier, vol. 179(C).
    7. 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.
    8. Janson, Svante, 2021. "On the probability that a binomial variable is at most its expectation," Statistics & Probability Letters, Elsevier, vol. 171(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel A. Griffith, 2022. "Reciprocal Data Transformations and Their Back-Transforms," Stats, MDPI, vol. 5(3), pages 1-24, July.
    2. Daniel A. Griffith, 2014. "Reply," The American Statistician, Taylor & Francis Journals, vol. 68(1), pages 67-69, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:86:y:2014:i:c:p:91-98. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.