On properties of the phase-type mixed Poisson process and its applications to reliability shock modeling

Dheeraj Goyal, Nil Kamal Hazra, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)
30 Downloads (Pure)

Abstract

Although Poisson processes are widely used in various applications for modeling of recurrent point events, there exist obvious limitations. Several specific mixed Poisson processes (which are formally not Poisson processes any more) that were recently introduced in the literature overcome some of these limitations. In this paper, we define a general mixed Poisson process with the phase-type (PH) distribution as the mixing one. As the PH distribution is dense in the set of lifetime distributions, the new process can be used to approximate any mixed Poisson process. We study some basic stochastic properties of the new process and discuss relevant applications by considering the extreme shock model, the stochastic failure rate model and the δ-shock model.
Original languageEnglish
JournalMethodology and Computing in Applied Probability
Early online date16 Jun 2022
DOIs
Publication statusE-pub ahead of print - 16 Jun 2022

Keywords

  • mixed Poisson process
  • non-homogeneous Poisson process
  • phase-type distribution
  • shock models

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