IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v52y2005i4p370-380.html
   My bibliography  Save this article

On the median residual lifetime and its aging properties: A characterization theorem and applications

Author

Listed:
  • Rosa E. Lillo

Abstract

This paper is devoted to study several aspects of the median residual life function (MERLF). In reliability studies, it is well known that, although the MERLF have several advantages over the mean residual life function (MRLF), the MRLF has the good property of uniquely determine a life distribution whereas either the median residual life function (MERLF) or an α‐percentile residual life do not have such good property. We shall give a characterization result where knowledge of both the MERLF and the survival function on an interval does uniquely determine the distribution. Moreover, in order to apply this characterization in practical situations, we propose a method to estimate the necessary information of the survival function. Relationships between analytical properties of the survival function and its associated MERLF are also obtained. Bryson and Siddiqui [J Am Statist Assoc 64 (1969), 1472–1483] proved relationships among seven criteria for aging, out of which two contained the MRLF (decreasing MRLF and net decreasing MRLF). In this paper, we prove that the same pattern of relationships holds if the MRLF is replaced by the MERLF. We also examine the aging criteria corresponding to an increasing MERLF and show that there is no relation between the behavior (increasing or decreasing) of the MERLF and of the MRLF. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005

Suggested Citation

  • Rosa E. Lillo, 2005. "On the median residual lifetime and its aging properties: A characterization theorem and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(4), pages 370-380, June.
    • Handle: RePEc:wly:navres:v:52:y:2005:i:4:p:370-380
    DOI: 10.1002/nav.20082
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20082
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20082?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
    ---><---

    References listed on IDEAS

    as
    1. Barry C. Arnold & Patrick L. Brockett, 1983. "Technical Note—When Does the βth Percentile Residual Life Function Determine the Distribution?," Operations Research, INFORMS, vol. 31(2), pages 391-396, April.
    2. Harry Joe & Frank Proschan, 1984. "Percentile Residual Life Functions," Operations Research, INFORMS, vol. 32(3), pages 668-678, June.
    3. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
    4. David C. Schmittlein & Donald G. Morrison, 1981. "The Median Residual Lifetime: A Characterization Theorem and an Application," Operations Research, INFORMS, vol. 29(2), pages 392-399, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M. Shafaei Noughabi & M. Kayid, 2019. "Bivariate quantile residual life: a characterization theorem and statistical properties," Statistical Papers, Springer, vol. 60(6), pages 2001-2012, December.
    2. M. Kayid & M. Shafaei Noughabi & A. M. Abouammoh, 2020. "A Nonparametric Estimator of Bivariate Quantile Residual Life Model with Application to Tumor Recurrence Data Set," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 237-253, April.

    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. Jong-Hyeon Jeong & Sin-Ho Jung & Joseph P. Costantino, 2008. "Nonparametric Inference on Median Residual Life Function," Biometrics, The International Biometric Society, vol. 64(1), pages 157-163, March.
    2. Sin-Ho Jung & Jong-Hyeon Jeong & Hanna Bandos, 2009. "Regression on Quantile Residual Life," Biometrics, The International Biometric Society, vol. 65(4), pages 1203-1212, December.
    3. M. Kayid & M. Shafaei Noughabi & A. M. Abouammoh, 2020. "A Nonparametric Estimator of Bivariate Quantile Residual Life Model with Application to Tumor Recurrence Data Set," Journal of Classification, Springer;The Classification Society, vol. 37(1), pages 237-253, April.
    4. M. Shafaei Noughabi & M. Kayid, 2019. "Bivariate quantile residual life: a characterization theorem and statistical properties," Statistical Papers, Springer, vol. 60(6), pages 2001-2012, December.
    5. repec:cte:wsrepe:ws102612 is not listed on IDEAS
    6. Jamal Bouoiyour & Refk Selmi, 2017. "The Bitcoin price formation: Beyond the fundamental sources," Working Papers hal-01548710, HAL.
    7. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    8. Christian E. Galarza & Panpan Zhang & Víctor H. Lachos, 2021. "Logistic Quantile Regression for Bounded Outcomes Using a Family of Heavy-Tailed Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 325-349, November.
    9. Xiangjin Shen & Shiliang Li & Hiroki Tsurumi, 2013. "Comparison of Parametric and Semi-Parametric Binary Response Models," Departmental Working Papers 201308, Rutgers University, Department of Economics.
    10. Tony Lancaster & Sung Jae Jun, 2010. "Bayesian quantile regression methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 287-307.
    11. Shaked, Moshe, 2010. "The decreasing percentile residual life aging notion," DES - Working Papers. Statistics and Econometrics. WS ws101807, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Genya Kobayashi & Hideo Kozumi, 2012. "Bayesian analysis of quantile regression for censored dynamic panel data," Computational Statistics, Springer, vol. 27(2), pages 359-380, June.
    13. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
    14. Xiangjin Shen & Iskander Karibzhanov & Hiroki Tsurumi & Shiliang Li, 2022. "Comparison of Bayesian and Sample Theory Parametric and Semiparametric Binary Response Models," Staff Working Papers 22-31, Bank of Canada.
    15. Sugawara, Shinya, 2012. "A nonparametric Bayesian approach for counterfactual prediction with an application to the Japanese private nursing home market," MPRA Paper 42154, University Library of Munich, Germany.
    16. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    17. Xianhua Dai & Wolfgang Karl Härdle & Keming Yu, 2016. "Do maternal health problems influence child's worrying status? Evidence from the British Cohort Study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2941-2955, December.
    18. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    19. Yixin Wang & Ying Qing Chen, 2019. "Estimating Attributable Life Expectancy Under the Proportional Mean Residual Life Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 659-676, December.
    20. repec:hum:wpaper:sfb649dp2014-021 is not listed on IDEAS
    21. Mani Suleiman & Haydar Demirhan & Leanne Boyd & Federico Girosi & Vural Aksakalli, 2022. "Bayesian prediction of emergency department wait time," Health Care Management Science, Springer, vol. 25(2), pages 275-290, June.
    22. Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2009. "New tests for exponentiality against new better than used in th quantile," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(1), pages 85-97.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:52:y:2005:i:4:p:370-380. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.