TY - JOUR
T1 - On a New Shot Noise Process and the Induced Survival Model
AU - Cha, Ji Hwan
AU - Finkelstein, Maxim
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - Traditionally, in applications, the shot noise processes have been studied under the assumption that the underlying arrival point process (shock process) is the homogeneous (or nonhomogeneous) Poisson process. However, most of the real life shock processes do not possess the independent increments property and the Poisson assumption is made just for simplicity. Recently, in the literature, a new point process, the generalized Polya process (GPP), has been proposed and characterized. The GPP is defined via the stochastic intensity that depends on the number of events in the previous interval and, therefore, does not possess the independent increments property. In this paper, we consider the GPP as an underlying shock process for the shot noise process. The corresponding survival model is considered and the survival probability and its failure rate are derived and thoroughly analyzed. Furthermore, a new concept, the history-dependent residual life time, is defined and discussed.
AB - Traditionally, in applications, the shot noise processes have been studied under the assumption that the underlying arrival point process (shock process) is the homogeneous (or nonhomogeneous) Poisson process. However, most of the real life shock processes do not possess the independent increments property and the Poisson assumption is made just for simplicity. Recently, in the literature, a new point process, the generalized Polya process (GPP), has been proposed and characterized. The GPP is defined via the stochastic intensity that depends on the number of events in the previous interval and, therefore, does not possess the independent increments property. In this paper, we consider the GPP as an underlying shock process for the shot noise process. The corresponding survival model is considered and the survival probability and its failure rate are derived and thoroughly analyzed. Furthermore, a new concept, the history-dependent residual life time, is defined and discussed.
KW - Failure rate
KW - Generalized Polya process
KW - History-dependent residual lifetime
KW - Poisson process
KW - Shot noise process
UR - http://www.scopus.com/inward/record.url?scp=85013031351&partnerID=8YFLogxK
U2 - 10.1007/s11009-017-9550-y
DO - 10.1007/s11009-017-9550-y
M3 - Article
AN - SCOPUS:85013031351
SN - 1387-5841
VL - 20
SP - 897
EP - 917
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 3
ER -