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

Ji Hwan Cha () and Massimiliano Giorgio ()
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Ji Hwan Cha: Ewha Womans University
Massimiliano Giorgio: University of Campania Luigi Vanvitelli

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1137-1154

Abstract: 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.

Keywords: Reliability; Complete intensity functions; Dependence structure; Marginal process; Shock model; Primary 60K10; Secondary 62P30 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11009-018-9633-4

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