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On generalized orderings and ageing classes for residual life and inactivity time at random time

Author

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  • Arijit Patra

    (Rajiv Gandhi Institute of Petroleum Technology)

  • Chanchal Kundu

    (Rajiv Gandhi Institute of Petroleum Technology)

Abstract

In this paper, we enhance the study of ageing classes and stochastic comparisons of residual life at random time (RLRT) and inactivity time at random time (ITRT). We provide some new preservation properties of generalized ageing classes (viz. s-IFR, s-DFR) and generalized stochastic ordering (s-FR) for RLRT and ITRT, where s is a non-negative integer. An application in reliability theory is also investigated. The results strengthen some results available in the literature and are expected to be useful in reliability theory, forensic science, econometrics, queueing theory and actuarial science.

Suggested Citation

  • Arijit Patra & Chanchal Kundu, 2019. "On generalized orderings and ageing classes for residual life and inactivity time at random time," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 691-704, August.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:6:d:10.1007_s00184-018-0701-0
    DOI: 10.1007/s00184-018-0701-0
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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. Dewan, Isha & Khaledi, Baha-Eldin, 2014. "On stochastic comparisons of residual life time at random time," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 73-79.
    3. K. T. Marshall, 1968. "Some Inequalities in Queuing," Operations Research, INFORMS, vol. 16(3), pages 651-668, June.
    4. Chanchal Kundu & Arijit Patra, 2018. "Some results on residual life and inactivity time at random time," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(2), pages 372-384, January.
    5. Félix Belzunce & Asok Nanda & Eva-María Ortega & José Ruiz, 2008. "Generalized orderings of excess lifetimes of renewal processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 297-310, August.
    6. Joag-dev, Kumar & Kochar, Subhash & Proschan, Frank, 1995. "A general composition theorem and its applications to certain partial orderings of distributions," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 111-119, February.
    7. Fagiuoli, E. & Pellerey, F., 1994. "Mean residual life and increasing convex comparison of shock models," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 337-345, August.
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    Cited by:

    1. Mansour Shrahili & Mohamed Kayid, 2022. "Characterizations of the Exponential Distribution by Some Random Hazard Rate Sequences," Mathematics, MDPI, vol. 10(17), pages 1-11, August.
    2. Arijit Patra & Chanchal Kundu, 2021. "Stochastic comparisons and ageing properties of residual lifetime mixture models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 123-143, August.

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