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.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference6 articles.
1. A stochastic process whose successive intervals between events form a first order Markov chain — I;Lampard;J. Appl. Prob.,1968
2. A branching process allowing immigration;Heathcote;J. R. Statist. Soc.,1965
3. Corrections and comments on the paper “A branching process with immigration”;Heathcote;J. R. Statist. Soc.,1966
4. Note on a certain family of discrete distributions
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. A queueing system with Markov-dependent arrivals;Journal of Applied Probability;1985-09
2. Some remarks on a counter process;Journal of Applied Probability;1976-09
3. Some remarks on a counter process;Journal of Applied Probability;1976-09