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.
Bibliographical noteFunding Information:
The authors thank the reviewers for helpful comments and advices. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2019R1A2B5B02069500). This work was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177).
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
- Poisson generalized gamma process
- generalized Pólya process
- positive dependence
- restarting property
- stochastic properties