IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v37y2022i4d10.1007_s00180-021-01176-2.html
   My bibliography  Save this article

Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling

Author

Listed:
  • Yusuf Can Sevil

    (Dokuz Eylul University)

  • Tugba Ozkal Yildiz

    (Dokuz Eylul University)

Abstract

In this paper, we consider three sampling methods that are ranked set sampling (RSS), generalized modified ranked set sampling (GMRSS) and extreme ranked set sampling (ERSS). RSS and ERSS are well-known sampling schemes. In GMRSS procedure, a single ranked unit is selected for full measurement. This paper improves estimators based on RSS, GMRSS and ERSS for association parameter of type-I Gumbel’s bivariate exponential distribution (GBED-I) by using maximum likelihood (ML) estimation. To determine whether there is a statistically significant association between the components, we investigate likelihood ratio tests based on RSS, MRSS and ERSS. To examine the performances of suggested estimators and tests with respect to their counterparts of simple random sampling (SRS), we provide an extensive Monte Carlo simulation. According to the results, it appears that GMRSS provides a more efficient ML estimator than the other sampling methods when only the maximum ranked units are selected. Also, it is observed that the test statistic based on GMRSS has the highest power among the test statistics when the sample is obtained from the maximum ranked units. Considering that GMRSS can be obtained with less effort than other samples, these results become even more meaningful.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:4:d:10.1007_s00180-021-01176-2
    DOI: 10.1007/s00180-021-01176-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-021-01176-2
    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/s00180-021-01176-2?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. Qinying He & H. Nagaraja & Chunjie Wu, 2013. "Efficient simulation of complete and censored samples from common bivariate exponential distributions," Computational Statistics, Springer, vol. 28(6), pages 2479-2494, December.
    2. 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.
    3. 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.
    4. Z. Abo-Eleneen & H. Nagaraja, 2002. "Fisher Information in an Order Statistic and its Concomitant," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 667-680, September.
    5. V. Barnett, 1985. "The Bivariate Exponential Distribution; A Review And Some New Results," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 39(4), pages 343-356, December.
    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. Modarres, Reza & Zheng, Gang, 2004. "Maximum likelihood estimation of dependence parameter using ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 315-323, July.
    8. Gang Zheng & Mohammad Al-Saleh, 2002. "Modified Maximum Likelihood Estimators Based on Ranked Set Samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 641-658, September.
    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. Rais Seki Lenzo & Jean-Pierre Kalay Kut & Kasongo Numbi Kashemukunda & Kaloucha Kanga Nsiama & Gradi Kalonji Lelo & Ange Kra & Aurelie Nkayulu Wa Luvuvamu & Kevin Lumpungu Lutumba, 2024. "Contribution To The Study Of Assessing Rainfall Patterns As Indicators Of Climate Change: A Study In Kinshasa City, Democratic Republic Of Congo," Geological Behavior (GBR), Zibeline International Publishing, vol. 8(2), pages 136-145, September.

    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. 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.
    2. Gang Zheng & Mohammad Al-Saleh, 2003. "Improving the best linear unbiased estimator for the scale parameter of symmetric distributions by using the absolute value of ranked set samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(3), pages 253-265.
    3. Amini, Morteza & Ahmadi, J., 2007. "Fisher information in record values and their concomitants about dependence and correlation parameters," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 964-972, June.
    4. 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.
    5. 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.
    6. Rajni Goel & Hare Krishna, 2022. "Statistical inference for two Lindley populations under balanced joint progressive type-II censoring scheme," Computational Statistics, Springer, vol. 37(1), pages 263-286, March.
    7. Hofmann, Glenn & Balakrishnan, N. & Ahmadi, Jafar, 2005. "Characterization of hazard function factorization by Fisher information in minima and upper record values," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 51-57, April.
    8. 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.
    9. Oualid Saci & Megdouda Ourbih-Tari & Leila Baiche, 2023. "Maximum Likelihood Estimation of Parameters of a Random Variable Using Monte Carlo Methods," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 540-571, February.
    10. Pierre-Olivier Goffard & Stéphane Loisel & Denys Pommeret, 2017. "Polynomial Approximations for Bivariate Aggregate Claims Amount Probability Distributions," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 151-174, March.
    11. Siyu Yang & Ansheng Deng & Hui Cui, 2023. "Statistical Image Watermark Algorithm for FAPHFMs Domain Based on BKF–Rayleigh Distribution," Mathematics, MDPI, vol. 11(23), pages 1-25, November.
    12. 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.
    13. 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.
    14. Hassen Muttlak & Walid Al-Sabah, 2003. "Statistical quality control based on ranked set sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(9), pages 1055-1078.
    15. Nadarajah Saralees & Kotz Samuel, 2006. "Determination of Software Reliability based on Multivariate Exponential, Lomax and Weibull Models," Monte Carlo Methods and Applications, De Gruyter, vol. 12(5), pages 447-459, November.
    16. 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.
    17. Wenchen Dai & Wangxue Chen & Honglve Zhao, 2025. "Estimation of the population mean under imperfect simple Z ranked set sampling," Statistical Papers, Springer, vol. 66(4), pages 1-22, June.
    18. 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.
    19. 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.
    20. 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.

    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:compst:v:37:y:2022:i:4:d:10.1007_s00180-021-01176-2. 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.