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On Cox processes and gamma renewal processes

Published online by Cambridge University Press:  14 July 2016

Nikos Yannaros
Nikos Yannaros*
Affiliation:
Royal Institute of Technology, Stockholm
*
∗Postal address: Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden.
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Abstract

It is shown that the gamma distribution with shape parameter α can be obtained through a p-thinning for every 0 < p < 1, when 0 < α ≦ 1. In the case α > 1, the gamma distribution cannot be obtained through thinning. The class of renewal processes with gamma-distributed times between events is considered. It is shown that an ordinary gamma renewal process is a Cox process if and only if 0 < α ≦ 1. Necessary and sufficient conditions for delayed gamma renewal processes to be Cox are also given. Finally, a short description of the gamma renewal process as a Cox process is given.

Keywords

POINT PROCESSESTHINNINGGAMMA DISTRIBUTIONINVERSES OF THINNED PROCESSES
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 423 - 427
Copyright
Copyright © Applied Probability Trust 1988 

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