IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v73y2019i4p367-374.html
   My bibliography  Save this article

Demystifying the Integrated Tail Probability Expectation Formula

Author

Listed:
  • Ambrose Lo

Abstract

Calculating the expected values of different types of random variables is a central topic in mathematical statistics. Targeted toward students and instructors in both introductory probability and statistics courses and graduate-level measure-theoretic probability courses, this pedagogical note casts light on a general expectation formula stated in terms of distribution and survival functions of random variables and discusses its educational merits. Often consigned to an end-of-chapter exercise in mathematical statistics textbooks with minimal discussion and presented under superfluous technical assumptions, this unconventional expectation formula provides an invaluable opportunity for students to appreciate the geometric meaning of expectations, which is overlooked in most undergraduate and graduate curricula, and serves as an efficient tool for the calculation of expected values that could be much more laborious by traditional means. For students’ benefit, this formula deserves a thorough in-class treatment in conjunction with the teaching of expectations. Besides clarifying some commonly held misconceptions and showing the pedagogical value of the expectation formula, this note offers guidance for instructors on teaching the formula taking the background of the target student group into account.

Suggested Citation

  • Ambrose Lo, 2019. "Demystifying the Integrated Tail Probability Expectation Formula," The American Statistician, Taylor & Francis Journals, vol. 73(4), pages 367-374, October.
    • Handle: RePEc:taf:amstat:v:73:y:2019:i:4:p:367-374
    DOI: 10.1080/00031305.2018.1497541
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2018.1497541
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00031305.2018.1497541?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.

    Citations

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


    Cited by:

    1. Carlos Alós-Ferrer & Michele Garagnani, 2022. "Who likes it more? Using response times to elicit group preferences in surveys," ECON - Working Papers 422, Department of Economics - University of Zurich.
    2. Chen, Le-Yu & Lee, Sokbae, 2023. "Sparse quantile regression," Journal of Econometrics, Elsevier, vol. 235(2), pages 2195-2217.
    3. Albrecher, Hansjörg & Cheung, Eric C.K. & Liu, Haibo & Woo, Jae-Kyung, 2022. "A bivariate Laguerre expansions approach for joint ruin probabilities in a two-dimensional insurance risk process," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 96-118.
    4. Liu, Yang, 2020. "A general treatment of alternative expectation formulae," Statistics & Probability Letters, Elsevier, vol. 166(C).

    More about this item

    Statistics

    Access and download statistics

    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:taf:amstat:v:73:y:2019:i:4:p:367-374. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UTAS20 .

    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.