Poisson generalized gamma process and its properties

Although the nonhomogeneous Poisson process has been intensively applied in practice, it has also its own limitations. In this paper, a new counting process model (called Poisson Generalized Gamma Process) is developed to overcome the limitations of the nonhomogeneous Poisson process. Initially, some basic stochastic properties are derived. It will be seen that this new counting process model includes both the generalized Pólya and Poisson Lindley processes as special cases. The influence of the model parameters on the behaviour of the new counting process model is analysed. The increments of the new process are shown to exhibit positive dependence properties. The corresponding compound process is defined and studied as well.