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Note on the reversible counters system of Lampard

Published online by Cambridge University Press:  14 July 2016

R. M. Phatarfod
R. M. Phatarfod*
Affiliation:
Monash University
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Abstract

The paper considers an extension to the reversible counters system of Lampard [1]. In Lampard's model the input processes are two independent Poisson processes; this results in a gamma Markov sequence for the time-interval between successive output pulses and a negative binomial Markov sequence for the counts at the times of out-put pulses. We consider the input process to be a bivariate Poisson process and show that the first out-put process given above is not affected, while the second out-put-process becomes of a type studied in the theory of branching processes.

Keywords

REVERSIBLE COUNTERSBIVARIATE POISSONGAMMA MARKOV SEQUENCEBRANCHING PROCESS WITH IMMIGRATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 624 - 628
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Lampard, D. G. (1968) A stochastic process whose successive intervals between events form a first order Markov chain — I. J. Appl. Prob. 5, 648–668.CrossRefGoogle Scholar
[2] Maritz, J. S. (1952) Note on a certain family of discrete distributions. Biometrika 39, 196–198.Google Scholar
[3] Bartlett, M. S. (1955) An introduction to Stochastic Processes. Cambridge University Press, Cambridge.Google Scholar
[4] Heathcote, C. R. (1965) A branching process allowing immigration. J. R. Statist. Soc. B 27, 138–143.Google Scholar
[5] Heathcote, C. R. (1966) Corrections and comments on the paper “A branching process with immigration”. J. R. Statist. Soc. B 28, 213–217.Google Scholar
[6] Pakes, A. G. (1971) On a theorem of Quine and Seneta for the Galton-Watson process with immigration. Austral. J. Statist. 13, 159–164.CrossRefGoogle Scholar