CHARACTERIZATION OF THE GENERALIZED POLYA PROCESS AND ITS APPLICATIONS

Abstract

In this paper some important properties of the generalized Polya process are derived and their applications are discussed. The generalized Polya process is defined based on the stochastic intensity. By interpreting the defined stochastic intensity of the generalized Polya 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 Polya 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.