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Characterization of the Generalized Pólya Process and its Applications

Part of: Special processes Applications

Published online by Cambridge University Press:  22 February 2016

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

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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.

Keywords

Generalized Pólya processrestarting propertydistribution of the number of eventsconditional arrival time distributionrepair typereliability application

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62P30: Applications in engineering and industry
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 4 , December 2014 , pp. 1148 - 1171
Copyright
© Applied Probability Trust 

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