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Coupon collector’s problems with statistical applications to rankings

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  • Sigeo Aki
  • Katuomi Hirano

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

Suggested Citation

  • Sigeo Aki & Katuomi Hirano, 2013. "Coupon collector’s problems with statistical applications to rankings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 571-587, June.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:3:p:571-587
    DOI: 10.1007/s10463-012-0382-9
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    Cited by:

    1. Kiyoshi Inoue & Sigeo Aki, 2014. "On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 895-920, October.

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