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

• Published in: Methodology and computing in applied probability Vol. 20; no. 4; pp. 1137 - 1154
• Main Authors: Cha, Ji Hwan, Giorgio, Massimiliano
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2018; Springer Nature B.V
• Subjects: Bivariate analysis; Business and Management; Computer based modeling; Economics; Electrical Engineering; Life Sciences; Mathematics and Statistics; Multivariate analysis; Production scheduling; Sequential scheduling; Statistics; Primary 60K10; Secondary 62P30; Complete intensity functions; Reliability; Marginal process; Shock model; Dependence structure
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-018-9633-4

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.