Poisson generalized gamma process and its properties

Ji Hwan Cha, Sophie Mercier

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish
Pages (from-to)1123-1140
Number of pages18
Issue number8
StatePublished - 2021

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  • Poisson generalized gamma process
  • generalized Pólya process
  • positive dependence
  • restarting property
  • stochastic properties


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