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The covariance of two type II counters

Published online by Cambridge University Press:  14 July 2016

Mark Berman
Mark Berman*
Affiliation:
CSIRO Division of Mathematics and Statistics, Sydney
*
∗Postal address: CSIRO Division of Mathematics and Statistics, P.O. Box 218, Lindfield, NSW 2070, Australia.
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Abstract

Consider three independent Poisson processes of point events of rates λ1, λ 2 and λ12. Suppose there are two electronic counters, the first recording events from the first and third Poisson processes, and the second recording events from the second and third Poisson processes. Both counters are subject to dead times of Type II, i.e. where all events, whether recorded or not, cause dead times. The covariance of the numbers of events recorded by the two counters in a suitable time period is derived. This extends earlier work of Cox and Isham (1977) and Kingman (1977) who considered the same problem for Type I counters, i.e. where only recorded events cause dead times.

Keywords

COVARIANCEPOINT PROCESSPOISSON PROCESSTYPE II COUNTER
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 3 , September 1981 , pp. 782 - 787
Copyright
Copyright © Applied Probability Trust 

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References

Abramowitz, M. and Stegun, I. A. (1970) Handbook of Mathematical Functions. Dover, New York.Google Scholar
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