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1 results

  • Characterization of the Generalized Pólya Process and its Applications

  • Part of
  • Ji Hwan Cha
  • Journal:
    Advances in Applied Probability / Volume 46 / Issue 4 / December 2014
    Published online by Cambridge University Press:
    22 February 2016, pp. 1148-1171
    Print publication:
    December 2014
    • Article
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  • 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.