Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aven T, Jensen U (1999) Stochastic models in reliability. Springer, New York
Badía FG, Lee H (2020) On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures. Metrika 83:355–375
Badía FG, Sangüesa C, Cha JH (2018) Univariate and multivariate stochastic comparisons and ageing properties of the generalized Pólya processes. J Appl Probab 55:233–253
Belzunce F, Lillo RE, Ruiz JM, Shaked M (2001) Stochastic comparisons of nonhomogeneous processes. Probab Eng Inform Sci 15:199–224
Cha JH (2014) Characterization of the generalized Polya process and its applications. Adv Appl Probab 46:1148–1171
Cha JH (2019) Poisson lindley process and its main properties. Stat Probab Lett 152:74–81
Cha JH, Mercier S (2021) Poisson generalized gamma process and its properties. Stochastics 93:1123–1140
Cha JH, Finkelstein M (2011) Stochastic intensity for minimal repairs in heterogeneous populations. J Appl Probab 48:868–876
Cha JH, Finkelstein M (2018) Point processes for reliability analysis. Springer, London
Lindley DV (1958) Fiducial distributions and bayes’ theorem. J Royal Stat Soc Ser B 20:102–107
Ross SM (2003) Introduction to probability models, 8th edn. Academic Press, San Diego
Navarro J, del Águila Y (2017) Stochastic comparisons of distorted distributions, coherent systems and mixtures with ordered components. Metrika 80:627–648
Navarro J (2018) Stochastic comparisons of coherent systems. Metrika 81:465–482
Shaked M, Shanthikumar JG (2007) Stochastic orders. Springer, New York
Acknowledgements
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).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Cha, J.H., Badía, F.G. Poisson generalized Lindley process and its properties. Metrika 87, 61–74 (2024). https://doi.org/10.1007/s00184-023-00906-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00184-023-00906-4
Keywords
- Poisson generalized lindley process
- Stochastic properties
- Restarting property
- Generalized polya process
- Positive dependence