Coupon collector’s problems with statistical applications to rankings

Sigeo Aki () and Katuomi Hirano

Annals of the Institute of Statistical Mathematics, 2013, vol. 65, issue 3, 587 pages

Abstract: Some new exact distributions on coupon collector’s waiting time problems are given based on a generalized Pólya urn sampling. In particular, usual Pólya urn sampling generates an exchangeable random sequence. In this case, an alternative derivation of the distribution is also obtained from de Finetti’s theorem. In coupon collector’s waiting time problems with $$m$$ kinds of coupons, the observed order of $$m$$ kinds of coupons corresponds to a permutation of $$m$$ letters uniquely. Using the property of coupon collector’s problems, a statistical model on the permutation group of $$m$$ letters is proposed for analyzing ranked data. In the model, as the parameters mean the proportion of the $$m$$ kinds of coupons, the observed ranking can be intuitively understood. Some examples of statistical inference are also given. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Keywords: Generalized Pólya urn; Dirichlet distribution; Exchangeability; Likelihood ratio test; Permutation (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10463-012-0382-9 (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:spr:aistmt:v:65:y:2013:i:3:p:571-587

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10463/PS2

DOI: 10.1007/s10463-012-0382-9

Access Statistics for this article

Annals of the Institute of Statistical Mathematics is currently edited by Tomoyuki Higuchi

More articles in Annals of the Institute of Statistical Mathematics from Springer, The Institute of Statistical Mathematics
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().