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Sequential rank and the Pólya urn

Published online by Cambridge University Press:  14 July 2016

Herbert Robbins and
John Whitehead
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.
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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.

Keywords

EXTREME VALUESORDER STATISTICSPÓLYA URNSEQUENTIAL RANK

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 1 , March 1979, pp. 213 - 219
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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