IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v63y2022i6d10.1007_s00362-022-01295-y.html
   My bibliography  Save this article

Exact prediction intervals for future exponential and Pareto lifetimes based on ordered ranked set sampling of non-random and random size

Author

Listed:
  • H. M. Barakat

    (Zagazig University)

  • Haidy A. Newer

    (Ain-Shams University)

Abstract

In the present paper, two pivotal statistics are suggested to construct prediction intervals of future observations from the exponential and Pareto distributions in the context of ordered ranked set sample. Our study encompasses two cases. The first case, when the sample size is assumed to be fixed and the second case when the sample size is assumed to be a positive integer-valued random variable. In addition to deriving explicit forms for the distribution functions of the two pivotal statistics, we consider some special cases for the random size of the sample. Moreover, a simulation study is carried out to assess the efficiency of the suggested methods. Finally, an example representing lifetime data is analyzed.

Suggested Citation

  • H. M. Barakat & Haidy A. Newer, 2022. "Exact prediction intervals for future exponential and Pareto lifetimes based on ordered ranked set sampling of non-random and random size," Statistical Papers, Springer, vol. 63(6), pages 1801-1827, December.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:6:d:10.1007_s00362-022-01295-y
    DOI: 10.1007/s00362-022-01295-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01295-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/s00362-022-01295-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. Mostafa M. Mohie El-Din & Mohamed S. Kotb & Ehab F. Abd-Elfattah & Haidy A. Newer, 2017. "Bayesian inference and prediction of the Pareto distribution based on ordered ranked set sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(13), pages 6264-6279, July.
    2. K. Raghunandanan & S. A. Patil, 1972. "On order statistics for random sample size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 26(4), pages 121-126, December.
    3. Wangxue Chen & Rui Yang & Dongsen Yao & Chunxian Long, 2021. "Pareto parameters estimation using moving extremes ranked set sampling," Statistical Papers, Springer, vol. 62(3), pages 1195-1211, June.
    4. H. M. Barakat & Y. H. Abdelkader, 2004. "Computing the moments of order statistics from nonidentical random variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 13(1), pages 15-26, April.
    5. Shah, Imtiyaz A. & Barakat, H.M. & Khan, A.H., 2020. "Characterizations through generalized and dual generalized order statistics, with an application to statistical prediction problem," Statistics & Probability Letters, Elsevier, vol. 163(C).
    6. H. M. Barakat & E. M. Nigm & Magdy E. El-Adll & M. Yusuf, 2018. "Prediction of future generalized order statistics based on exponential distribution with random sample size," Statistical Papers, Springer, vol. 59(2), pages 605-631, June.
    7. Lynne Stokes, 1995. "Parametric ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 465-482, September.
    8. Adatia, A., 2000. "Estimation of parameters of the half-logistic distribution using generalized ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 33(1), pages 1-13, March.
    9. 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. Heba F. Nagy & Amer Ibrahim Al-Omari & Amal S. Hassan & Ghadah A. Alomani, 2022. "Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data," Mathematics, MDPI, vol. 10(21), pages 1-19, November.
    2. Kotb Mohammed S., 2016. "Bayesian Prediction Bounds for the Exponential-Type Distribution Based on Ordered Ranked Set Sampling," Stochastics and Quality Control, De Gruyter, vol. 31(1), pages 45-54, June.
    3. 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.
    4. Barabesi, Lucio & El-Sharaawi, Abdel, 2001. "The efficiency of ranked set sampling for parameter estimation," Statistics & Probability Letters, Elsevier, vol. 53(2), pages 189-199, June.
    5. El-Adll, Magdy E., 2011. "Predicting future lifetime based on random number of three parameters Weibull distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1842-1854.
    6. Xiaoyue Zhao & Zehua Chen, 2002. "On the Ranked-Set Sampling M-Estimates for Symmetric Location Families," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 626-640, September.
    7. Oktay Karabağ & Barış Tan, 2018. "Analysis of a group purchasing organization under demand and price uncertainty," Flexible Services and Manufacturing Journal, Springer, vol. 30(4), pages 844-883, December.
    8. 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.
    9. N. Balakrishnan & M. Brito & A. Quiroz, 2013. "On the goodness-of-fit procedure for normality based on the empirical characteristic function for ranked set sampling data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 161-177, February.
    10. Dinesh S. Bhoj, 2001. "Ranked Set Sampling with Unequal Samples," Biometrics, The International Biometric Society, vol. 57(3), pages 957-962, September.
    11. Vic Barnett & Maria Cecilia Mendes Barreto, 2001. "Estimators for a Poisson parameter using ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(8), pages 929-941.
    12. 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.
    13. Mostata Razmkhah & Jafar Ahmadi, 2012. "Statistical inference based on the top scores," METRON, Springer;Sapienza Università di Roma, vol. 70(1), pages 89-107, April.
    14. Jiang, Jun & Shang, Pengjian & Zhang, Zuoquan & Li, Xuemei, 2018. "The multi-scale high-order statistical moments of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 474-488.
    15. Jesse Frey & Timothy G. Feeman, 2017. "Efficiency comparisons for partially rank-ordered set sampling," Statistical Papers, Springer, vol. 58(4), pages 1149-1163, December.
    16. Raqab, Mohammad Z. & Kouider, Elies & Al-Shboul, Qasim M., 2002. "Best linear invariant estimators using ranked set sampling procedure: comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 97-105, March.
    17. Abdelkader, Yousry H., 2011. "A Laplace transform method for order statistics from nonidentical random variables and its application in Phase-type distribution," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1143-1149, August.
    18. Saralees Nadarajah, 2006. "Explicit expressions for moments of beta order statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 377-384.
    19. Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    20. Hlynka, M. & Brill, P.H. & Horn, W., 2010. "A method for obtaining Laplace transforms of order statistics of Erlang random variables," Statistics & Probability Letters, Elsevier, vol. 80(1), pages 9-18, January.

    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:63:y:2022:i:6:d:10.1007_s00362-022-01295-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.