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A non-renewal process with renewal counting distributions

Published online by Cambridge University Press:  01 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
The University of Arizona
*
∗Postal address: Systems and Industrial Engineering, The University of Arizona, Tucson, AZ 85721, USA.
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Abstract

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A simple example is given of a point process with dependent inter-event intervals for which the distributions of the counting random variables Nt are given by the same formulas as for a renewal process. This example shows the care needed in establishing that a given point process has the renewal property, but also raises interesting questions about the class of point processes with given counting distributions.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 19 , Issue 1 , March 1987 , pp. 287 - 288
Copyright
Copyright © Applied Probability Trust 1987 

References

1. Chandramohan, J. and Liang, L-K. (1985) Bernoulli, multinomial and Markov chain thinning of some point processes and some results about the superposition of dependent renewal processes. J. Appl. Prob. 22, 828–835.CrossRefGoogle Scholar
2. Whitt, W. (1987) Stochastic ordering. In Encyclopedia of Statistical Sciences, Vol. 7, ed. Kotz, S. and Johnson, N. L., Wiley, New York.Google Scholar