IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i1d10.1007_s00362-022-01314-y.html
   My bibliography  Save this article

A ranked-based estimator of the mean past lifetime with an application

Author

Listed:
  • Elham Zamanzade

    (University of Isfahan)

  • Majid Asadi

    (University of Isfahan)

  • Afshin Parvardeh

    (University of Isfahan)

  • Ehsan Zamanzade

    (University of Isfahan)

Abstract

The mean past lifetime (MPL) is an important tool in reliability and survival analysis for measuring the average time elapsed since the occurrence of an event, under the condition that the event has occurred before a specific time $$t>0$$ t > 0 . This article develops a nonparametric estimator for MPL based on observations collected according to ranked set sampling (RSS) design. It is shown that the proposed estimator is a strongly uniform consistent estimator of MPL. It is also proved that the introduced estimator tends to a Gaussian process under some mild conditions. A Monte Carlo simulation study is employed to evaluate the performance of the proposed estimator with its competitor in simple random sampling (SRS). Our findings show the introduced estimator is more efficient than its counterpart estimator in SRS as long as the quality of ranking is better than random. Finally, an illustrative example is provided to describe the potential application of the developed estimator in assessing the average time between the infection and diagnosis in HIV patients.

Suggested Citation

  • Elham Zamanzade & Majid Asadi & Afshin Parvardeh & Ehsan Zamanzade, 2023. "A ranked-based estimator of the mean past lifetime with an application," Statistical Papers, Springer, vol. 64(1), pages 161-177, February.
  • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01314-y
    DOI: 10.1007/s00362-022-01314-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01314-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00362-022-01314-y?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. Afshin Parvardeh, 2015. "A note on the asymptotic distribution of the estimation of the mean past lifetime," Statistical Papers, Springer, vol. 56(1), pages 205-215, February.
    2. Frey, Jesse & Ozturk, Omer & Deshpande, Jayant V., 2007. "Nonparametric Tests for Perfect Judgment Rankings," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 708-717, June.
    3. Zamanzade, Ehsan & Mahdizadeh, M., 2017. "A more efficient proportion estimator in ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 28-33.
    4. M. Mahdizadeh & Ehsan Zamanzade, 2018. "A new reliability measure in ranked set sampling," Statistical Papers, Springer, vol. 59(3), pages 861-891, September.
    5. Hani M. Samawi & Haresh Rochani & Daniel Linder & Arpita Chatterjee, 2017. "More efficient logistic analysis using moving extreme ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 753-766, March.
    6. Abdul Haq & Jennifer Brown & Elena Moltchanova & Amer Ibrahim Al‐Omari, 2013. "Partial ranked set sampling design," Environmetrics, John Wiley & Sons, Ltd., vol. 24(3), pages 201-207, May.
    7. Xinlei Wang & Johan Lim & Lynne Stokes, 2016. "Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1576-1590, October.
    8. Zamanzade, Elham & Parvardeh, Afshin & Asadi, Majid, 2019. "Estimation of mean residual life based on ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 35-55.
    9. Xiaofang He & Wangxue Chen & Wenshu Qian, 2020. "Maximum likelihood estimators of the parameters of the log-logistic distribution," Statistical Papers, Springer, vol. 61(5), pages 1875-1892, October.
    10. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188, May.
    11. Wenshu Qian & Wangxue Chen & Xiaofang He, 2021. "Parameter estimation for the Pareto distribution based on ranked set sampling," Statistical Papers, Springer, vol. 62(1), pages 395-417, 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. Zeinab Akbari Ghamsari & Ehsan Zamanzade & Majid Asadi, 2024. "Using nomination sampling in estimating the area under the ROC curve," Computational Statistics, Springer, vol. 39(5), pages 2721-2742, July.
    2. Zamanzade, Elham & Parvardeh, Afshin & Asadi, Majid, 2019. "Estimation of mean residual life based on ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 35-55.
    3. Ehsan Zamanzade & M. Mahdizadeh & Hani M. Samawi, 2020. "Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 485-502, September.
    4. Xinlei Wang & Ke Wang & Johan Lim, 2012. "Isotonized CDF Estimation from Judgment Poststratification Data with Empty Strata," Biometrics, The International Biometric Society, vol. 68(1), pages 194-202, March.
    5. Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    6. Cesar Augusto Taconeli & Suely Ruiz Giolo, 2020. "Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data," Computational Statistics, Springer, vol. 35(4), pages 1827-1851, December.
    7. M. Mahdizadeh & Ehsan Zamanzade, 2022. "New insights on goodness-of-fit tests for ranked set samples," Statistical Papers, Springer, vol. 63(6), pages 1777-1799, December.
    8. Zamanzade, Ehsan & Wang, Xinlei, 2017. "Estimation of population proportion for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 257-269.
    9. M. Mahdizadeh & Ehsan Zamanzade, 2018. "Interval estimation of $$P(X," Computational Statistics, Springer, vol. 33(3), pages 1325-1348, September.
    10. Ehsan Zamanzade & Michael Vock, 2018. "Some nonparametric tests of perfect judgment ranking for judgment post stratification," Statistical Papers, Springer, vol. 59(3), pages 1085-1100, September.
    11. Zamanzade, Ehsan & Vock, Michael, 2015. "Variance estimation in ranked set sampling using a concomitant variable," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 1-5.
    12. Michael Weba & Nora Dörmann, 2017. "Application of the delta method to functions of the sample mean when observations are dependent," Statistical Papers, Springer, vol. 58(4), pages 957-986, December.
    13. Rehman Syed Abdul & Shabbir Javid, 2021. "On the improvement of paired ranked set sampling to estimate population mean," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 193-205, September.
    14. Ehsan Zamanzade, 2019. "EDF-based tests of exponentiality in pair ranked set sampling," Statistical Papers, Springer, vol. 60(6), pages 2141-2159, December.
    15. Mozhgan Alirezaei Dizicheh & Nasrollah Iranpanah & Ehsan Zamanzade, 2021. "Bootstrap Methods for Judgment Post Stratification," Statistical Papers, Springer, vol. 62(5), pages 2453-2471, October.
    16. Nader Gemayel & Elizabeth Stasny & James Tackett & Douglas Wolfe, 2012. "Ranked set sampling: an auditing application," Review of Quantitative Finance and Accounting, Springer, vol. 39(4), pages 413-422, November.
    17. Omer Ozturk & Steven MacEachern, 2004. "Order restricted randomized designs for control versus treatment comparison," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(4), pages 701-720, December.
    18. Omer Ozturk, 2019. "Two-stage cluster samples with ranked set sampling designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 63-91, February.
    19. Hassan Amal S. & Elshaarawy Rasha S. & Nagy Heba F., 2022. "Parameter estimation of exponentiated exponential distribution under selective ranked set sampling," Statistics in Transition New Series, Polish Statistical Association, vol. 23(4), pages 37-58, December.
    20. M. Mahdizadeh & Ehsan Zamanzade, 2020. "Estimating asymptotic variance of M-estimators in ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1785-1803, December.

    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:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01314-y. 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.