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An extended class of univariate and multivariate generalized Pólya processes

Part of: Applications Stochastic processes

Published online by Cambridge University Press:  11 July 2022

Ji Hwan Cha
Ji Hwan Cha*
Affiliation:
Ewha Womans University
*
*Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email: jhcha@ewha.ac.kr
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Abstract

In this paper, we consider an extended class of univariate and multivariate generalized Pólya processes and study its properties. In the generalized Pólya process considered in [8], each occurrence of an event increases the stochastic intensity of the counting process. In the extended class studied in this paper, on the contrary, it decreases the stochastic intensity of the process, which induces a kind of negative dependence in the increments in the disjoint time intervals. First, we define the extended class of generalized Pólya processes and derive some preliminary results which will be used in the remaining part of the paper. It is seen that the extended class of generalized Pólya processes can be viewed as generalized pure death processes, where the death rate depends on both the state and the time. Based on the preliminary results, the main properties of the multivariate extended generalized Pólya process and meaningful characterizations are obtained. Finally, possible applications to reliability modeling are briefly discussed.

Keywords

Extended generalized Pólya processpure death processrestarting propertymixture counting processreliability application

MSC classification

Primary: 60G55: Point processes
Secondary: 62P30: Applications in engineering and industry
Type
Original Article
Information
Advances in Applied Probability , Volume 54 , Issue 3 , September 2022 , pp. 974 - 997
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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