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Univariate and multivariate stochastic comparisons and ageing properties of the generalized Pólya process

Part of: Special processes Distribution theory - Probability

Published online by Cambridge University Press:  28 March 2018

F. G. Badía ,
C. Sangüesa  and
Ji Hwan Cha
F. G. Badía*
Affiliation:
University of Zaragoza
C. Sangüesa*
Affiliation:
University of Zaragoza
Ji Hwan Cha*
Affiliation:
Ewha Womans University
*
* Postal address: Department of Statistical Methods, University of Zaragoza, Zaragoza, 50009, Spain.
* Postal address: Department of Statistical Methods, University of Zaragoza, Zaragoza, 50009, Spain.
**** Postal address: Department of Statistics, Ewha Womans University, Seoul, 120-750, Korea. Email address: jhcha@ewha.ac.kr
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Abstract

In this work we consider the generalized Pólya process with baseline intensity function r and parameters α and β recently studied by Cha (2014). The aim of this work is to provide both univariate and multivariate stochastic comparisons between two generalized Pólya processes with different baseline intensity functions and the same parameters α and β for the epoch and inter-epoch times of the two processes. The comparisons are analogous to stochastic comparisons in Belzunce et al. (2001) for two nonhomogeneous Poisson or pure-birth processes with different intensity functions. Moreover, we study both univariate and multivariate ageing properties of the epoch and inter-epoch times of the generalized Pólya process.

Keywords

Generalized Pólya processepoch timestochastic orderageing propertygeneralized order statistics

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 1 , March 2018 , pp. 233 - 253
Copyright
Copyright © Applied Probability Trust 2018 

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