Correct Ordering in the Zipf--Poisson Ensemble
AbstractRankings 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Journal of the American Statistical Association.
Volume (Year): 107 (2012)
Issue (Month): 500 (December)
Contact details of provider:
Web page: http://www.tandfonline.com/UASA20
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Michael McNulty).
If references are entirely missing, you can add them using this form.