Probabilistic sampling of finite renewal processes
Nelson Antunes and Vladas Pipiras
Source: Bernoulli Volume 17, Number 4
(2011), 1285-1326.
Abstract
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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Keywords: IP flows; finite renewal process; interrenewal times; number of renewals; sampling; thinning; asymptotic normality; decompounding
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Permanent link to this document: http://projecteuclid.org/euclid.bj/1320417505
Digital Object Identifier: doi:10.3150/10-BEJ321
Zentralblatt MATH identifier: 1229.62111
Mathematical Reviews number (MathSciNet): MR2854773
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