Probabilistic sampling of finite renewal processes

Details Probabilistic sampling of finite renewal processes Probabilistic sampling of finite renewal processes

2012-01-05

arxiv.org/abs/1201.1076v1

Bernoulli 2011, Vol. 17, No. 4, 1285-1326

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ321 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ321

Consider a finite renewal process in the sense that interrenewal times are positive i.i.d. variables and the total number of renewals is a random variable, independent of interrenewal times. A finite point process can be obtained by probabilistic sampling of the finite renewal process, where each renewal is sampled with a fixed probability and independently of other renewals. The problem addressed in this work concerns statistical inference of the original distributions of the total number of renewals and interrenewal times from a sample of i.i.d. finite point processes obtained by sampling finite renewal processes. This problem is motivated by traffic measurements in the Internet in order to characterize flows of packets (which can be seen as finite renewal processes) and where the use of packet sampling is becoming prevalent due to increasing link speeds and limited storage and processing capacities.

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