TY - JOUR
T1 - Poisson Lindley process and its main properties
AU - Cha, Ji Hwan
N1 - 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.
PY - 2019/9
Y1 - 2019/9
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.
KW - Compound Poisson Lindley process
KW - Poisson Lindley process
KW - Positive dependence
KW - Stochastic processes
KW - Stochastic properties
UR - http://www.scopus.com/inward/record.url?scp=85065721982&partnerID=8YFLogxK
U2 - 10.1016/j.spl.2019.04.008
DO - 10.1016/j.spl.2019.04.008
M3 - Article
AN - SCOPUS:85065721982
SN - 0167-7152
VL - 152
SP - 74
EP - 81
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
ER -