A method for estimating intensity of a Poisson process.

摘要

Motivated by its vast applications, we investigate ways to estimate the intensity of a Poisson process. Much of the work on modeling and analysis of repairable systems is based on the assumption of a special type of nonhomogeneous Poisson process (NHPP) known as Weibull process or Power-law process. In this thesis, we link the traditional homogeneous and nonhomogeneous Poisson processes to the classical time series via a sequence of the empirical recurrence rates (ERR), calculated at equally spaced intervals of time. We consider a computationally simple algorithm to calculate the total area and also the area for the last ten recurrence rates under the ERR curve. We conclude that the mean function of an NHPP can be estimated from the ERR values. In addition, we argue by simulation, that the algorithm can be implemented to forecast NHPP observations with various forms of intensity function. A correction factor is defined based on the overall trend of the targeted point process.