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Article Dans Une Revue Stochastics: An International Journal of Probability and Stochastic Processes Année : 2021

Poisson Generalized Gamma Process and Its Properties

Résumé

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 behavior of the new counting process model is analyzed. The increments of the new process are shown to exhibit positive dependence properties. The corresponding compound process is defined and studied as well.
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Dates et versions

hal-03085128 , version 1 (21-12-2020)

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Ji Hwan Cha, Sophie Mercier. Poisson Generalized Gamma Process and Its Properties. Stochastics: An International Journal of Probability and Stochastic Processes, 2021, 93 (8), pp.1123-1140. ⟨10.1080/17442508.2020.1868469⟩. ⟨hal-03085128⟩
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