IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i21p4102-d962468.html
   My bibliography  Save this article

Improved Estimation of the Inverted Kumaraswamy Distribution Parameters Based on Ranked Set Sampling with an Application to Real Data

Author

Listed:
  • Heba F. Nagy

    (Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

  • Amer Ibrahim Al-Omari

    (Department of Mathematics, Faculty of Science, Al Al-Bayt University, Mafraq 25113, Jordan)

  • Amal S. Hassan

    (Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

  • Ghadah A. Alomani

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

The ranked set sampling (RSS) methodology is an effective technique of acquiring data when measuring the units in a population is costly, while ranking them is easy according to the variable of interest. In this article, we deal with an RSS-based estimation of the inverted Kumaraswamy distribution parameters, which is extensively applied in life testing and reliability studies. Some estimation techniques are regarded, including the maximum likelihood, the maximum product of spacing’s, ordinary least squares, weighted least squares, Cramer–von Mises, and Anderson–Darling. We demonstrate a simulation investigation to assess the performance of the suggested RSS-based estimators via accuracy measures relative to simple random sampling. On the basis of actual data regarding the waiting times between 65 consecutive eruptions of Kiama Blowhole, additional conclusions have been drawn. The outcomes of simulation and real data application demonstrated that RSS-based estimators outperformed their simple random sampling counterparts significantly based on the same number of measured units.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4102-:d:962468
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/21/4102/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/21/4102/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jianping Zhu & Hua Xin & Chenlu Zheng & Tzong-Ru Tsai, 2021. "Inference for the Process Performance Index of Products on the Basis of Power-Normal Distribution," Mathematics, MDPI, vol. 10(1), pages 1-14, December.
    2. Monjed H. Samuh & Amer I. Al-Omari & Nursel Koyuncu, 2020. "Estimation Of The Parameters Of The New Weibull-Pareto Distribution Using Ranked Set Sampling," Statistica, Department of Statistics, University of Bologna, vol. 80(1), pages 103-123.
    3. Rashad Bantan & Mahmoud Elsehetry & Amal S. Hassan & Mohammed Elgarhy & Dreamlee Sharma & Christophe Chesneau & Farrukh Jamal, 2021. "A Two-Parameter Model: Properties and Estimation under Ranked Sampling," Mathematics, MDPI, vol. 9(11), pages 1-16, May.
    4. Amer Ibrahim Al-Omari & Amal S. Hassan & Naif Alotaibi & Mansour Shrahili & Heba F. Nagy, 2021. "Reliability Estimation of Inverse Lomax Distribution Using Extreme Ranked Set Sampling," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-12, December.
    5. 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.
    6. 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.
    7. Kin Lam & Bimal Sinha & Zhong Wu, 1994. "Estimation of parameters in a two-parameter exponential distribution using ranked set sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 723-736, December.
    8. Nóra Chuív & Bimal Sinha & Zhong Wu, 1995. "Estimation of the location parameter of a Cauchy distribution using a ranked set sample," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 234-235, December.
    9. 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.
    10. Amer Ibrahim Al-Omari & SidAhmed Benchiha & Ibrahim M. Almanjahie, 2021. "Efficient Estimation of the Generalized Quasi-Lindley Distribution Parameters under Ranked Set Sampling and Applications," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-17, July.
    11. 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.
    12. Cesar Augusto Taconeli & Wagner Hugo Bonat, 2020. "On the performance of estimation methods under ranked set sampling," Computational Statistics, Springer, vol. 35(4), pages 1805-1826, December.
    13. 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.
    14. 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.
    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. Safar M. Alghamdi & Rashad A. R. Bantan & Amal S. Hassan & Heba F. Nagy & Ibrahim Elbatal & Mohammed Elgarhy, 2022. "Improved EDF-Based Tests for Weibull Distribution Using Ranked Set Sampling," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    2. Jorge Figueroa-Zúñiga & Juan G. Toledo & Bernardo Lagos-Alvarez & Víctor Leiva & Jean P. Navarrete, 2023. "Inference Based on the Stochastic Expectation Maximization Algorithm in a Kumaraswamy Model with an Application to COVID-19 Cases in Chile," Mathematics, MDPI, vol. 11(13), pages 1-14, June.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Manoj Chacko, 2017. "Bayesian estimation based on ranked set sample from Morgenstern type bivariate exponential distribution when ranking is imperfect," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(3), pages 333-349, April.
    8. Dinesh S. Bhoj, 2001. "Ranked Set Sampling with Unequal Samples," Biometrics, The International Biometric Society, vol. 57(3), pages 957-962, September.
    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. 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.
    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. Cesar Augusto Taconeli & Idemauro Antonio Rodrigues Lara, 2022. "Improved confidence intervals based on ranked set sampling designs within a parametric bootstrap approach," Computational Statistics, Springer, vol. 37(5), pages 2267-2293, November.
    13. 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.
    14. 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.
    15. Yusuf Can Sevil & Tugba Ozkal Yildiz, 2022. "Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling," Computational Statistics, Springer, vol. 37(4), pages 1695-1726, September.
    16. Mohamed S. Abdallah & Amer I. Al-Omari & Naif Alotaibi & Ghadah A. Alomani & A. S. Al-Moisheer, 2022. "Estimation of distribution function using L ranked set sampling and robust extreme ranked set sampling with application to reliability," Computational Statistics, Springer, vol. 37(5), pages 2333-2362, November.
    17. Manoj Chacko & P. Thomas, 2008. "Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(2), pages 301-318, June.
    18. Chen, Wangxue & Xie, Minyu & Wu, Ming, 2013. "Parametric estimation for the scale parameter for scale distributions using moving extremes ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2060-2066.
    19. David E. Giles, 2009. "Bias Reduction for the Maximum Likelihood Estimator of the Scale Parameter in the Half-Logistic Distribution," Econometrics Working Papers 0901, Department of Economics, University of Victoria.
    20. Fengshi Zhang & Wenhao Gui, 2020. "Parameter and Reliability Inferences of Inverted Exponentiated Half-Logistic Distribution under the Progressive First-Failure Censoring," Mathematics, MDPI, vol. 8(5), pages 1-29, May.

    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:gam:jmathe:v:10:y:2022:i:21:p:4102-:d:962468. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.