Poisson Lindley process and its main properties

Ji Hwan Cha

doi:10.1016/j.spl.2019.04.008

Poisson Lindley process and its main properties

Ji Hwan Cha

Department of Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	74-81
Number of pages	8
Journal	Statistics and Probability Letters
Volume	152
DOIs	https://doi.org/10.1016/j.spl.2019.04.008
State	Published - Sep 2019

Bibliographical note

Funding 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 ).

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Compound Poisson Lindley process
Poisson Lindley process
Positive dependence
Stochastic processes
Stochastic properties

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10.1016/j.spl.2019.04.008

Cite this

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abstract = "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.",

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N2 - 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.

AB - 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.

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JO - Statistics and Probability Letters

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Poisson Lindley process and its main properties

Abstract

Bibliographical note

Keywords

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