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Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Author

Listed:
  • Antonio Di Crescenzo

    (Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy)

  • Patrizia Di Gironimo

    (Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Fisciano (SA), Italy)

Abstract

We consider a suitable replacement model for random lifetimes, in which at a fixed time an item is replaced by another one having the same age but different lifetime distribution. We focus first on stochastic comparisons between the involved random lifetimes, in order to assess conditions leading to an improvement of the system. Attention is also given to the relative ratio of improvement, which is proposed as a suitable index finalized to measure the goodness of the replacement procedure. Finally, we provide various results on the dynamic differential entropy of the lifetime of the improved system.

Suggested Citation

  • Antonio Di Crescenzo & Patrizia Di Gironimo, 2018. "Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model," Mathematics, MDPI, vol. 6(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:10:p:204-:d:175865
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    References listed on IDEAS

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    1. Amarjit Kundu & Asok K. Nanda, 2016. "On study of dynamic survival and cumulative past entropies," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(1), pages 104-122, January.
    2. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    3. Laurence A. Baxter, 1982. "Reliability applications of the relevation transform," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(2), pages 323-330, June.
    4. Hon Ng & Jorge Navarro & Narayanaswamy Balakrishnan, 2012. "Parametric inference from system lifetime data under a proportional hazard rate model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 367-388, April.
    5. Ebrahimi, Nader & Kirmani, S.N.U.A. & Soofi, Ehsan S., 2007. "Multivariate dynamic information," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 328-349, February.
    6. Asok Nanda & Prasanta Paul, 2006. "Some Properties of Past Entropy and their Applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(1), pages 47-61, August.
    7. Asadi, Majid & Ebrahimi, Nader, 2000. "Residual entropy and its characterizations in terms of hazard function and mean residual life function," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 263-269, September.
    8. J. G. Shanthikumar & Laurence A. Baxter, 1985. "Closure properties of the relevation transform," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 32(1), pages 185-189, February.
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