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On a stopping time of Starr and its use in estimating the number of transmission sources

Published online by Cambridge University Press:  14 July 2016

Yehuda Vardi
Yehuda Vardi*
Affiliation:
Bell Laboratories
*
∗Postal address: Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974, U.S.A.
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Abstract

Consider N sources, each of which transmits signals according to a renewal process with a common, known, underlying distribution. Sequential point estimators for N, which are asymptotically efficient in comparison to the best fixed stopping strategy, are derived. Confidence statements for N, and applications to the problem of estimating finite populations are discussed.

The exact limiting distribution, and moments, of the stopping time we use, which was suggested by Starr, are derived.

Keywords

FINITE POPULATIONSSEQUENTIAL ESTIMATIONPOISSON PROCESSRENEWAL PROCESSTRANSMISSION SOURCES
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 235 - 242
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

This research was partially done at Cornell University and was supported by the following grants: NSF Grant MCS 75 22481, U.S. Army Research Office Contract DAAG29–73–C0008, and Office of Naval Research Contract N00014–75–C–0586.

References

[1] Starr, N. (1974) Optimal and adaptive stopping based on capture rates. J. Appl. Prob. 11, 294–301.Google Scholar
[2] Marcus, R. and Blumenthal, S. (1974) A sequential screening procedure. Technometrics 16, 229–234.Google Scholar