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Preservation properties of a homogeneous Poisson process stopped at an independent random time

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  • Salehi, E.T.
  • Badía, F.G.
  • Asadi, M.

Abstract

To study the ageing and stochastic properties of lifetime random variables, several classes of lifetime distributions have been defined in reliability literature. In this context, an interesting problem is then to investigate the closure properties of such classes under different operators. In this paper, we study the preservation properties of classes of increasing mean inactivity time (IMIT), increasing variance inactivity time (IVIT), and some other recently introduced classes, such as NRBU, NRBUE, and NBRUrh, under a Poisson process stopped at a random time. We also analyze the preservation properties of Poisson shock models for the above-mentioned ageing classes.

Suggested Citation

  • Salehi, E.T. & Badía, F.G. & Asadi, M., 2012. "Preservation properties of a homogeneous Poisson process stopped at an independent random time," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 574-585.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:3:p:574-585
    DOI: 10.1016/j.spl.2011.11.006
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    References listed on IDEAS

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    1. Ramesh C. Gupta, 2006. "Variance residual life function in reliability studies," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 343-355.
    2. S. Goliforushani & M. Asadi, 2008. "On the discrete mean past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 209-217, September.
    3. Abouammoh, A. M. & Ahmad, R. & Khalique, A., 2000. "On new renewal better than used classes of life distributions," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 189-194, June.
    4. Xiaohu Li & Maochao Xu, 2008. "Reversed hazard rate order of equilibrium distributions and a related aging notion," Statistical Papers, Springer, vol. 49(4), pages 749-767, October.
    5. M. Khorashadizadeh & A. H. Rezaei Roknabadi & G. R. Mohtashami Borzadaran, 2010. "Variance residual life function in discrete random ageing," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-75.
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    3. Rauwolf, Diana & Kamps, Udo, 2026. "Asymptotic behavior of renewal processes with random time," Statistics & Probability Letters, Elsevier, vol. 230(C).

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