Selective interaction of a Poisson and renewal process: first-order stationary point results
- 1 August 1970
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 7 (2) , 359-372
- https://doi.org/10.2307/3211970
Abstract
The simple stationarity of a previously derived equilibrium process of responses in a renewal inhibited stationary point process is established by deriving the joint distribution of the number of responses in contiguous intervals in the process. For a renewal inhibited Poisson process the variancetime function of the process is obtained; the distribution of an arbitrary between-response interval and the synchronous counting distribution are also derived following analytic justification of the required results. These results strengthen earlier results in the theory of stationary point processes. Three other point processes arising from the interaction are briefly discussed.Keywords
This publication has 5 references indexed in Scilit:
- Selective interaction of a stationary point process and a renewal processJournal of Applied Probability, 1970
- On Streams of Events and Mixtures of StreamsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1966
- The Statistical Analysis of Series of EventsPublished by Springer Nature ,1966
- Selective interaction of two independent recurrent processesJournal of Applied Probability, 1965
- On the Lengths of Intervals in a Stationary Point ProcessJournal of the Royal Statistical Society Series B: Statistical Methodology, 1962