IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v73y2019i1p56-60.html
   My bibliography  Save this article

Sum of a Random Number of Correlated Random Variables that Depend on the Number of Summands

Author

Listed:
  • Joel E. Cohen

Abstract

The mean and variance of a sum of a random number of random variables are well known when the number of summands is independent of each summand and when the summands are independent and identically distributed (iid), or when all summands are identical. In scientific and financial applications, the preceding conditions are often too restrictive. Here, we calculate the mean and variance of a sum of a random number of random summands when the mean and variance of each summand depend on the number of summands and when every pair of summands has the same correlation. This article shows that the variance increases with the correlation between summands and equals the variance in the iid or identical cases when the correlation is zero or one.

Suggested Citation

  • Joel E. Cohen, 2019. "Sum of a Random Number of Correlated Random Variables that Depend on the Number of Summands," The American Statistician, Taylor & Francis Journals, vol. 73(1), pages 56-60, January.
    • Handle: RePEc:taf:amstat:v:73:y:2019:i:1:p:56-60
    DOI: 10.1080/00031305.2017.1311283
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2017.1311283
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00031305.2017.1311283?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. Andrew Y. Chen, 2021. "The Limits of p‐Hacking: Some Thought Experiments," Journal of Finance, American Finance Association, vol. 76(5), pages 2447-2480, October.

    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:1:p:56-60. 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.