Characterization of the generalized Pólya process and its applications

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Abstract

In this paper some important properties of the generalized Pólya process are derived and their applications are discussed. The generalized Pólya process is defined based on the stochastic intensity. By interpreting the defined stochastic intensity of the generalized Pólya process, the restarting property of the process is discussed. Based on the restarting property of the process, the joint distribution of the number of events is derived and the conditional joint distribution of the arrival times is also obtained. In addition, some properties of the compound process defined for the generalized Pólya process are derived. Furthermore, a new type of repair is defined based on the process and its application to the area of reliability is discussed. Several examples illustrating the applications of the obtained properties to various areas are suggested.

Original languageEnglish
Pages (from-to)1148-1171
Number of pages24
JournalAdvances in Applied Probability
Volume46
Issue number4
DOIs
StatePublished - 1 Dec 2014

Bibliographical note

Publisher Copyright:
© Applied Probability Trust 2014.

Keywords

  • Conditional arrival time distribution
  • Distribution of the number of events
  • Generalized Pólya process
  • Reliability application
  • Repair type
  • Restarting property

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