IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v23y2022i4p37-58n12.html
   My bibliography  Save this article

Parameter estimation of exponentiated exponential distribution under selective ranked set sampling

Author

Listed:
  • Hassan Amal S.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt .)

  • Elshaarawy Rasha S.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt .)

  • Nagy Heba F.

    (Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt .)

Abstract

Partial ranked set sampling (PRSS) is a cost-effective sampling method. It is a combination of simple random sample (SRS) and ranked set sampling (RSS) designs. The PRSS method allows flexibility for the experimenter in selecting the sample when it is either difficult to rank the units within each set with full confidence or when experimental units are not available. In this article, we introduce and define the likelihood function of any probability distribution under the PRSS scheme. The performance of the maximum likelihood estimators is examined when the available data are assumed to have an exponentiated exponential (EE) distribution via some selective RSS schemes as well as SRS. The suggested ranked schemes include the PRSS, RSS, neoteric RSS (NRSS), and extreme RSS (ERSS). An intensive simulation study was conducted to compare and explore the behaviour of the proposed estimators. The study demonstrated that the maximum likelihood estimators via PRSS, NRSS, ERSS, and RSS schemes are more efficient than the corresponding estimators under SRS. A real data set is presented for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:vrs:stintr:v:23:y:2022:i:4:p:37-58:n:12
    DOI: 10.2478/stattrans-2022-0041
    as

    Download full text from publisher

    File URL: https://doi.org/10.2478/stattrans-2022-0041
    Download Restriction: no
    File URL: https://libkey.io/10.2478/stattrans-2022-0041?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. M. A. Sabry & M. Shaaban, 2020. "Dependent Ranked Set Sampling Designs for Parametric Estimation with Applications," Annals of Data Science, Springer, vol. 7(2), pages 357-371, June.
    2. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
    3. Amal S. Hassan & Rasha S. Elshaarawy & Ronald Onyango & Heba F. Nagy & Nawab Hussain, 2022. "Estimating System Reliability Using Neoteric and Median RSS Data for Generalized Exponential Distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-17, March.
    4. Walid Abu-Dayyeh & Aissa Assrhani & Kamarulzaman Ibrahim, 2013. "Estimation of the shape and scale parameters of Pareto distribution using ranked set sampling," Statistical Papers, Springer, vol. 54(1), pages 207-225, February.
    5. 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.
    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. 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.
    2. Gauss Cordeiro & Elizabeth Hashimoto & Edwin Ortega & Marcelino Pascoa, 2012. "The McDonald extended distribution: properties and applications," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(3), pages 409-433, July.
    3. Sanku Dey & Mahdi Salehi & Jafar Ahmadi, 2017. "Rayleigh distribution revisited via ranked set sampling," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 69-85, April.
    4. Amal S. Hassan & Ibrahim M. Almanjahie & Amer Ibrahim Al-Omari & Loai Alzoubi & Heba Fathy Nagy, 2023. "Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    5. 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.
    6. Mehrzad Ghorbani & Seyed Fazel Bagheri & Mojtaba Alizadeh, 2017. "A New Family of Distributions: The Additive Modified Weibull Odd Log-logistic-G Poisson Family, Properties and Applications," Annals of Data Science, Springer, vol. 4(2), pages 249-287, June.
    7. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy, 2020. "On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    8. Manal M. Yousef & Amal S. Hassan & Abdullah H. Al-Nefaie & Ehab M. Almetwally & Hisham M. Almongy, 2022. "Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    9. 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.
    10. 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.
    11. Jesse Frey & Timothy G. Feeman, 2017. "Efficiency comparisons for partially rank-ordered set sampling," Statistical Papers, Springer, vol. 58(4), pages 1149-1163, December.
    12. Debasis Kundu, 2022. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 575-595, November.
    13. Saralees Nadarajah & Gauss Cordeiro & Edwin Ortega, 2013. "The exponentiated Weibull distribution: a survey," Statistical Papers, Springer, vol. 54(3), pages 839-877, August.
    14. Debasis Kundu, 2021. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Papers 2201.02568, arXiv.org.
    15. 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.
    16. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    17. Samanta, Debashis & Kundu, Debasis, 2018. "Order restricted inference of a multiple step-stress model," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 62-75.
    18. Syed Abdul Rehman & Javid Shabbir, 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.
    19. Debashis Samanta & Debasis Kundu & Ayon Ganguly, 2018. "Order Restricted Bayesian Analysis of a Simple Step Stress Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-221, November.
    20. Amer Ibrahim Al-Omari & SidAhmed Benchiha & Ibrahim M. Almanjahie, 2022. "Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design," Mathematics, MDPI, vol. 10(17), pages 1-18, 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:vrs:stintr:v:23:y:2022:i:4:p:37-58:n:12. 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: Peter Golla (email available below). General contact details of provider: https://www.sciendo.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.