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Sequential rank and the Pólya urn

Published online by Cambridge University Press:  14 July 2016

Herbert Robbins*
Affiliation:
Columbia University
John Whitehead
Affiliation:
Chelsea College, University of London
*
Postal address: Department of Mathematical Statistics, Columbia University, New York, N.Y. 10027, U.S.A.

Abstract

A sequence of independent, identically distributed random variables is observed. After a sample of m has been collected attention is fixed to a particular observation. In this paper the fluctuations of the rank of this observation, as sampling continues, will be studied.

The process can be modelled by a Pólya urn scheme, and new results are obtained which are of interest in both sequential rank and Pólya urn contexts.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

∗∗

Present address: Department of Applied Statistics, The University, Whiteknights, Reading RG6 2AN, U.K.

References

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