Until now, the nonhomogeneous Poisson process has been intensively applied in various practical applications due to its merits. However, at the same time, it has also critical limitations in applications. To overcome these limitations, a new counting process model (called Poisson Lindley Process) is developed. It will be shown that this new counting process model does not have such limitations. Some basic stochastic properties are derived. In addition, a new concept for positive dependent increments is defined and the dependence structure is analyzed. Some of the properties obtained in this paper will be stated in general forms. One of the important contributions of this paper is to provide a new counting process model which allows explicit expression of the likelihood function.
Bibliographical noteFunding Information:
The author would like to thank the referee for very careful review, valuable comments and constructive suggestions. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211 ).
© 2019 Elsevier B.V.
- Compound Poisson Lindley process
- Poisson Lindley process
- Positive dependence
- Stochastic processes
- Stochastic properties