TY - JOUR
T1 - Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model
AU - Cha, Ji Hwan
AU - Giorgio, Massimiliano
N1 - Funding Information:
Acknowledgments The authors would like to thank the Editor and referees for helpful comments and valuable suggestions, which have improved the presentation of this paper considerably. The authors acknowledge that one of the referees’ insightful advice has led Theorem 2 to a more general result on association. The work of the first author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). The work of the first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211).
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/12/1
Y1 - 2018/12/1
N2 - In this paper, we develop a new class of bivariate counting processes that have ‘marginal regularity’ property. But, the ‘pooled processes’ in the developed class of bivariate counting processes are not regular. Therefore, the proposed class of processes allows simultaneous occurrences of two types of events, which can be applicable in practical modeling of counting events. Initially, some basic properties of the new class of bivariate counting processes will be discussed. Based on the obtained properties, the joint distributions of the numbers of events in time intervals will be derived and the dependence structure of the bivariate process will be discussed. Furthermore, the marginal and conditional processes will be studied. The application of the proposed bivariate counting process to a shock model will also be considered. In addition, the generalization to the multivariate counting processes will be discussed briefly.
AB - In this paper, we develop a new class of bivariate counting processes that have ‘marginal regularity’ property. But, the ‘pooled processes’ in the developed class of bivariate counting processes are not regular. Therefore, the proposed class of processes allows simultaneous occurrences of two types of events, which can be applicable in practical modeling of counting events. Initially, some basic properties of the new class of bivariate counting processes will be discussed. Based on the obtained properties, the joint distributions of the numbers of events in time intervals will be derived and the dependence structure of the bivariate process will be discussed. Furthermore, the marginal and conditional processes will be studied. The application of the proposed bivariate counting process to a shock model will also be considered. In addition, the generalization to the multivariate counting processes will be discussed briefly.
KW - Complete intensity functions
KW - Dependence structure
KW - Marginal process
KW - Reliability
KW - Shock model
UR - http://www.scopus.com/inward/record.url?scp=85045057431&partnerID=8YFLogxK
U2 - 10.1007/s11009-018-9633-4
DO - 10.1007/s11009-018-9633-4
M3 - Article
AN - SCOPUS:85045057431
SN - 1387-5841
VL - 20
SP - 1137
EP - 1154
JO - Methodology and Computing in Applied Probability
JF - Methodology and Computing in Applied Probability
IS - 4
ER -