Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model

Ji Hwan Cha; Massimiliano Giorgio

doi:10.1007/s11009-018-9633-4

Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model

Ji Hwan Cha, Massimiliano Giorgio

Department of Statistics

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

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1137-1154
Number of pages	18
Journal	Methodology and Computing in Applied Probability
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/s11009-018-9633-4
State	Published - 1 Dec 2018

Bibliographical note

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.

Keywords

Complete intensity functions
Dependence structure
Marginal process
Reliability
Shock model

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10.1007/s11009-018-9633-4

Cite this

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abstract = "In this paper, we develop a new class of bivariate counting processes that have {\textquoteleft}marginal regularity{\textquoteright} property. But, the {\textquoteleft}pooled processes{\textquoteright} 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.",

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Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model

Abstract

Bibliographical note

Keywords

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