  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.
