IDEAS home Printed from
   My bibliography  Save this article

Correct Ordering in the Zipf--Poisson Ensemble


  • Justin S. Dyer
  • Art B. Owen


Rankings based on counts are often presented to identify popular items, such as baby names, English words, or Web sites. This article shows that, in some examples, the number of correctly identified items can be very small. We introduce a standard error versus rank plot to diagnose possible misrankings. Then to explain the slowly growing number of correct ranks, we model the entire set of count data via a Zipf--Poisson ensemble with independent X i ∼ Poi( Ni -super-− α) for α > 1 and N > 0 and integers i ⩾ 1. We show that as N → ∞, the first n ′( N ) random variables have their proper order relative to each other, with probability tending to 1 for n ′ up to ( AN /log ( N ))-super-1/(α + 2) for A = α-super-2(α + 2)/4. We also show that the rate N -super-1/(α + 2) cannot be achieved. The ordering of the first n ′( N ) entities does not preclude for some interloping m > n ′. However, we show that the first n ″ random variables are correctly ordered exclusive of any interlopers, with probability tending to 1 if n ″ ⩽ ( BN /log ( N ))-super-1/(α + 2) for any B > A . We also show how to compute the cutoff for alternative models such as a Zipf--Mandelbrot--Poisson ensemble.

Suggested Citation

  • Justin S. Dyer & Art B. Owen, 2012. "Correct Ordering in the Zipf--Poisson Ensemble," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1510-1517, December.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1510-1517
    DOI: 10.1080/01621459.2012.734177

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    More about this item


    Access and download statistics


    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:jnlasa:v:107:y:2012:i:500:p:1510-1517. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Chris Longhurst). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.