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

F. G. Badía, C. Sangüesa, Ji Hwan Cha

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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.

Original languageEnglish
Pages (from-to)233-253
Number of pages21
JournalJournal of Applied Probability
Volume55
Issue number1
DOIs
StatePublished - 1 Mar 2018

Bibliographical note

Publisher Copyright:
Copyright © Applied Probability Trust 2018.

Keywords

  • Generalized Pólya process
  • ageing property
  • epoch time
  • generalized order statistics
  • stochastic order

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