IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i10p1547-1551.html
   My bibliography  Save this article

Only the first term of some series counts

Author

Listed:
  • Spataru, Aurel

Abstract

Let X,X1,X2,... be i.i.d. random variables, and set Sn=X1+...+Xn. We prove that for three important distributions of X, namely normal, exponential and geometric, series of the type [summation operator]n>=1anP(Sn>=xbn) or [summation operator]n>=1anP(Sn>=xbn) behave like their first term as x-->[infinity].

Suggested Citation

  • Spataru, Aurel, 2011. "Only the first term of some series counts," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1547-1551, October.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1547-1551
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211001878
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Pruss, Alexander R., 1997. "A two-sided estimate in the Hsu--Robbins--Erdös law of large numbers," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 173-180, October.
    Full references (including those not matched with items on IDEAS)

    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. Aurel Spătaru, 1999. "Precise Asymptotics in Spitzer's Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 12(3), pages 811-819, July.
    2. Bing-Yi Jing & Han-Ying Liang, 2008. "Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables," Journal of Theoretical Probability, Springer, vol. 21(4), pages 890-909, December.
    3. Liu, Weidong & Lin, Zhengyan, 2006. "Precise asymptotics for a new kind of complete moment convergence," Statistics & Probability Letters, Elsevier, vol. 76(16), pages 1787-1799, October.
    4. A. Spătaru, 2004. "Exact Asymptotics in log log Laws for Random Fields," Journal of Theoretical Probability, Springer, vol. 17(4), pages 943-965, October.

    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:81:y:2011:i:10:p:1547-1551. 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.