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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
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

Blackwell, D. and Kendall, D. (1964) The Martin boundary for Polya's urn scheme, and an application to stochastic population growth. J. Appl. Prob. 1, 284–296.Google Scholar
Groeneveld, R. and Meeden, G. (1977) The mode, median and mean inequality. Amer. Statistician 31, 120–121.Google Scholar
Gumbel, E. J. (1958) Statistics of Extremes. Columbia University Press, New York.CrossRefGoogle Scholar
Harris, L. B. (1952) On a limiting case for the distribution of exceedances, with an application to life testing. Ann. Math. Statist. 23, 295–298.Google Scholar
Wald, A. (1947) Sequential Analysis. Wiley, New York.Google Scholar