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A NOTE ON THE CLASS OF GEOMETRIC COUNTING PROCESSES

Published online by Cambridge University Press:  28 March 2013

Ji Hwan Cha  and
Maxim Finkelstein
Ji Hwan Cha
Affiliation:
Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea E-mail: [email protected]
Maxim Finkelstein
Affiliation:
Department of Mathematical Statistics, University of the Free State, 339 Bloemfontein 9300, South Africa E-mail: [email protected] and Max Planck Institute for Demographic Research, Rostock, Germany
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Abstract

In this paper, we suggest a new class of counting processes, called the Class of Geometric Counting Processes (CGCP), where each member of the counting process in the class has increments described by the geometric distribution. Distinct from the Poisson process, they do not possess the property of independent increments, which usually complicates probabilistic analysis. The suggested CGCP is defined and the dependence structure shared by the members of the class is discussed. As examples of useful applications, we consider stochastic survival models under external shocks. We show that the corresponding survival probabilities under reasonable assumptions can be effectively described by the CGCP without specifying the dependence structure.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 2 , April 2013 , pp. 177 - 185
Copyright
Copyright © Cambridge University Press 2013

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