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The inverses of thinned renewal processes

Published online by Cambridge University Press:  14 July 2016

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

The class of inverses of a p-thinned renewal process is considered. It is shown that this class consists of renewal processes. It consists of Cox and renewal processes if and only if the given thinned process is Cox and renewal. In the non-Cox case, there exists a unique top renewal process, which by thinning generates all the possible inverses. Conditions for a renewal process to be a top process are given. Finally, a gamma renewal process is shown to be a top process when α > 1, where α is the shape parameter of the gamma distribution.

Keywords

POINT PROCESSTHINNED POINT PROCESSINVERSE THINNINGCOX PROCESSGAMMA RENEWAL PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 822 - 828
Copyright
Copyright © Applied Probability Trust 1988 

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