Correct Ordering in the Zipf--Poisson Ensemble

Justin S. Dyer and Art B. Owen

Journal of the American Statistical Association, 2012, vol. 107, issue 500, 1510-1517

Abstract: 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.

Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2012.734177 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:107:y:2012:i:500:p:1510-1517

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2012.734177

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().