In spite of the practical usefulness of the nonhomogeneous Poisson process, it still has some restrictions. To overcome these restrictions, the Poisson Lindley process has been recently developed and introduced in Cha (Stat Probab Lett 152: 74–81, 2019). In this paper, we further generalize the Poisson Lindley process, so that the developed counting process model should have the restarting property and it should include the generalized Polya process as a special case. Some basic stochastic properties of the developed counting process model are derived. Dependence properties and stochastic comparisons are also discussed under a more general framework.
Bibliographical noteFunding Information:
The authors greatly thank the reviewers for helpful comments and advice. The work of the first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant Number: 2019R1A6A1A11051177). The work of the second author was funded by the Spanish government research project PGC2018-094964- B-100:PID2021-123737NB-100 (MINECO-FEDER).
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
- Generalized polya process
- Poisson generalized lindley process
- Positive dependence
- Restarting property
- Stochastic properties