IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v70y2012i2p121-131.html
   My bibliography  Save this article

On quantile reversed residual lifetime and its aging properties

Author

Listed:
  • Mervat Mahdy
  • Ramadan Mahdy

Abstract

If the random variable T denotes the lifetime (T > 0, with probability one) of a unit, then the random variable T (t) =[t − T|T ⩽ t],, for a fixed t, is known as the inactivity time or the reversed residual lifetime. In this paper, we define a new class of life distributions based on the quantile of the random variable T( t ) and study its reliability properties. Some new results of the proposed class are demonstrated including some closure properties. In particular, the quantile reversed residual lifetime functions of some well-known life distributions are illustrated. Finally, we define a new stochastic ordering based on the quantile reversed residual lifetime and study its reliability properties and closure properties. Copyright Sapienza Università di Roma 2012

Suggested Citation

  • Mervat Mahdy & Ramadan Mahdy, 2012. "On quantile reversed residual lifetime and its aging properties," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 121-131, August.
    • Handle: RePEc:spr:metron:v:70:y:2012:i:2:p:121-131
    DOI: 10.1007/BF03321970
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF03321970
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF03321970?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Mark Bebbington & Chin‐Diew Lai & Ričardas Zitikis, 2008. "Reduction in mean residual life in the presence of a constant competing risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(1), pages 51-63, January.
    3. Abu-Youssef, S. E., 2002. "A moment inequality for decreasing (increasing) mean residual life distributions with hypothesis testing application," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 171-177, April.
    4. Xiaohu Li & Jing Chen, 2004. "Aging properties of the residual life length of k‐out‐of‐n systems with independent but non‐identical components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 20(2), pages 143-153, April.
    5. Frostig, Esther, 2006. "On risk dependence and mrl ordering," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 231-243, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frostig, Esther, 2006. "On risk dependence and mrl ordering," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 231-243, February.
    2. Bebbington, Mark & Lai, Chin-Diew & Zitikis, RiÄ ardas, 2009. "Balancing burn-in and mission times in environments with catastrophic and repairable failures," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1314-1321.
    3. Al-Zahrani, Bander & Stoyanov, Jordan, 2008. "Moment inequalities for DVRL distributions, characterization and testing for exponentiality," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1792-1799, September.
    4. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).
    5. C. Satheesh Kumar & S. Dharmaja, 2014. "On some properties of Kies distribution," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 97-122, April.
    6. MARK BEBBINGTON & CHIN-DIEW LAI & RIcARDAS ZITIKIS, 2011. "Modelling Deceleration in Senescent Mortality," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(1), pages 18-37.
    7. Di Crescenzo, Antonio & Ricciardi, Luigi M., 1996. "Comparing first-passage times for semi-Markov skip-free processes," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 247-256, October.
    8. Sepehrifar, Mohammad B. & Khorshidian, Kavoos & Jamshidian, Ahmad R., 2015. "On renewal increasing mean residual life distributions: An age replacement model with hypothesis testing application," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 117-122.
    9. S. Gurler, 2012. "On residual lifetimes in sequential (n − k + 1)-out-of-n systems," Statistical Papers, Springer, vol. 53(1), pages 23-31, February.
    10. Belzunce, Félix & Ortega, Eva & Ruiz, José M., 1999. "The Laplace order and ordering of residual lives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 145-156, April.
    11. Kandil Abd El-Fattah Mohamed & Kayid Mohamed & Mahdy Mervat Mahdy Ramadan, 2010. "Median Inactivity Time Function and its Reliability Properties," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 253-268, January.
    12. Krzysztof Jasiński, 2021. "Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1241-1251, November.
    13. Sengupta, Debasis & Das, Sudipta, 2016. "Sharp bounds on DMRL and IMRL classes of life distributions with specified mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 101-107.
    14. Anis Mohammed Z., 2010. "On Testing Exponentiality Against DMRL Alternatives," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 281-299, January.
    15. 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.
    16. Scarsini, Marco & Shaked, Moshe, 2000. "On the value of an item subject to general repair or maintenance," European Journal of Operational Research, Elsevier, vol. 122(3), pages 625-637, May.
    17. Suchandan Kayal, 2018. "On Weighted Generalized Cumulative Residual Entropy of Order n," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 487-503, June.
    18. Pellerey, Franco, 1995. "On the preservation of some orderings of risks under convolution," Insurance: Mathematics and Economics, Elsevier, vol. 16(1), pages 23-30, April.
    19. Moghaddass, Ramin & Zuo, Ming J. & Wang, Wenbin, 2011. "Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth–death process," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 489-496.
    20. Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metron:v:70:y:2012:i:2:p:121-131. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.