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.

尽管非均质泊松过程已在实践中得到广泛应用，但它也有其自身的局限性。本文提出了一种新的计数过程模型（称为泊松广义伽玛过程），以克服非均匀泊松过程的局限性。最初，得出一些基本的随机属性。可以看出，这种新的计数过程模型包括广义的Pólya过程和Poisson Lindley过程，这是特例。分析了模型参数对新计数过程模型行为的影响。新过程的增量显示出正依赖性属性。还定义和研究了相应的复合过程。