IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v152y2019icp156-161.html
   My bibliography  Save this article

The density flatness phenomenon

Author

Listed:
  • Alhakim, Abbas
  • Molchanov, S.

Abstract

This paper investigates a curious phenomenon of some positive random variables having a constant density in some initial subinterval of their support. We discuss two methods of obtaining such a random variable with partly flat density. The main method is to sum powers of independent uniform variables with the number of terms matching the power. We show that the limit of this sum is an interesting infinitely divisible distribution and we study its basic properties, find a differential equation for its density, and obtain a recursive relation satisfied by its moments which allows for the calculation of its moment generating function and cumulants.

Suggested Citation

  • Alhakim, Abbas & Molchanov, S., 2019. "The density flatness phenomenon," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 156-161.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:156-161
    DOI: 10.1016/j.spl.2019.05.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521930135X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2019.05.006?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. Weissman, Ishay, 2017. "Sum of squares of uniform random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 147-154.
    2. Forrester, Peter J., 2018. "Comment on “Sum of squares of uniform random variables” by I. Weissman," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 118-122.
    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. Weissman, Ishay, 2023. "Some comments on “The density flatness phenomenon” by Alhakim and Molchanov and the Dickman distribution," Statistics & Probability Letters, Elsevier, vol. 194(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. Weissman, Ishay, 2023. "Some comments on “The density flatness phenomenon” by Alhakim and Molchanov and the Dickman distribution," Statistics & Probability Letters, Elsevier, vol. 194(C).
    2. Forrester, Peter J., 2018. "Comment on “Sum of squares of uniform random variables” by I. Weissman," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 118-122.

    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:152:y:2019:i:c:p:156-161. 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.