Note on Superposition of Renewal Processes - Suyono Suyono; J.A.M. van der Weide (Institut Teknologi Bandung, 2010)
In this paper we discuss distributional properties of superposition of renewal processes. Firstly, as a special case, we discuss probability distributions of a superposition of Poisson processes and its generalization, namely the sum of independent compound Poisson processes. In this case we have explicit expressions for their probability distributions. Secondly, we discuss the statistical moments of general superposition of renewal processes. We also discuss the statistical moments of the sum of independent renewal reward processes, a generalization of a supervision of renewal processes. The results are presented in the form of Laplace transforms. Finally we present the distributions of recurrence times of a superposition of renewal processes.