Search Advanced

AIMS Mathematics

2022, Volume 7, Issue 6: 10609-10624. doi: 10.3934/math.2022592
Previous Article Next Article
Research article

Improved generalized class of estimators in estimating the finite population mean using two auxiliary variables under two-stage sampling

  • 1.
    Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan
  • 2.
    Department of Statistics, Quaid-i-azam University, Islamabad, Pakistan
  • 3.
    Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
  • 4.
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
  • 5.
    Department of Statistics, Yazd University, P.O. Box 89175-741, Yazd, Iran
  • 6.
    Statistics Department, Faculty of Science, King Abdul Aziz University, Jeddah, Kingdom of Saudi Arabia
  • Received: 18 January 2022 Revised: 13 March 2022 Accepted: 24 March 2022 Published: 29 March 2022

  • MSC : 62D05

  • This article addresses the problem of estimating the finite population mean using two auxiliary variables under two-stage sampling scheme. Further the proposed improved class of estimators are provided their genralized form. Mathematical properties of the existing and proposed improved generalized class of estimators are derived up to first order of approximation. We identified 11 members of the improved generalized class of estimators which are more efficient than existing estimators in terms of the percentage relative efficiency. We use two real data sets under two-stage sampling to compare the performances of all of considered estimators.

    Citation: Sohaib Ahmad, Sardar Hussain, Javid Shabbir, Muhammad Aamir, M. El-Morshedy, Zubair Ahmad, Sharifah Alrajhi. Improved generalized class of estimators in estimating the finite population mean using two auxiliary variables under two-stage sampling[J]. AIMS Mathematics, 2022, 7(6): 10609-10624. doi: 10.3934/math.2022592

    Related Papers:

  • This article addresses the problem of estimating the finite population mean using two auxiliary variables under two-stage sampling scheme. Further the proposed improved class of estimators are provided their genralized form. Mathematical properties of the existing and proposed improved generalized class of estimators are derived up to first order of approximation. We identified 11 members of the improved generalized class of estimators which are more efficient than existing estimators in terms of the percentage relative efficiency. We use two real data sets under two-stage sampling to compare the performances of all of considered estimators.


    加载中


    [1] M. S. Ahmed, Some estimators for a finite population mean under two-stage sampling using multivariate auxiliary information, Appl. Math. Comput., 153 (2004), 505–511. https://doi.org/10.1016/S0096-3003(03)00651-9 doi: 10.1016/S0096-3003(03)00651-9
    [2] S. Bahl, R. Tuteja, Ratio and product type exponential estimators, J. Inform. Optim. Sci., 12 (1991), 159–164. https://doi.org/10.1080/02522667.1991.10699058 doi: 10.1080/02522667.1991.10699058
    [3] M. Hossain, M. S. Ahmed, A class of predictive estimators in two-stage sampling using auxiliary information, Int. J. Inform. Manage. Sci., 12 (2001), 49–56.
    [4] S. Hussain, S. Ahmad, M. Saleem, S. Akhtar, Finite population distribution function estimation with dual use of auxiliary information under simple and stratified random sampling, Plos One, 15 (2020), e0239098. https://doi.org/10.1371/journal.pone.0239098 doi: 10.1371/journal.pone.0239098
    [5] S. S. Mishra, B. Pradhan, Chain ratio estimator in two stage sampling, J. Reliab. Stat. Stud., 8 (2015).
    [6] P. Panda, Some strategies in two stage sampling using auxiliary information, Utkal University, 1998.
    [7] T. Rao, On certail methods of improving ration and regression estimators, Commun. Stat.-Theor. M., 20 (1991), 3325–3340. https://doi.org/10.1080/03610929108830705 doi: 10.1080/03610929108830705
    [8] L. N. Sahoo, N. Mahapatra, S. C. Senapati, A generalized method of estimation for two-stage sampling using two auxiliary variables, J. Stat. Theor. Pract., 3 (2009), 831–839. https://doi.org/10.1080/15598608.2009.10411963 doi: 10.1080/15598608.2009.10411963
    [9] S. Hussain, M. Zichuan, S. Hussain, A. Iftikhar, M. Asif, S. Akhtar, et al., On estimation of distribution function using dual auxiliary information under nonresponse using simple random sampling, J. Probab. Stat., 2020, 1693612. https://doi.org/10.1155/2020/1693612 doi: 10.1155/2020/1693612
    [10] L. Sahoo, C. Senapati, G. N. Singh, An alternative class of estimators in two-stage sampling with two auxiliary variables, Qual. Control Appl. Stat., 52 (2007), 489–490.
    [11] C. E. Särdnal, B. Swensson, J. Wretman, Model assisted survey sampling, Springer, 1992. https://doi.org/10.1007/978-1-4612-4378-6
    [12] T. Smith, A note on ratio estimates in multi-stage sampling, J. R. Stat. Soc. Series A, 1969,426–430. https://doi.org/10.2307/2344121 doi: 10.2307/2344121
    [13] M. Srivastava, N. Garg, A general class of estimators of a finite population mean using multi-auxiliary information under two stage sampling scheme, J. Reliab. Stat. Stud., 1 (2009), 103–118.
    [14] H. Nawaz, M. Rabia, A. Amir, M. Aslam, Two-stage sampling exponential and chain ratio type estimators in the presence of measurement error, J. Stat. Manag. Syst., 2021, 1–16. https://doi.org/10.1080/09720510.2021.1933708 doi: 10.1080/09720510.2021.1933708
    [15] A. Haq, M. Abbas, M. Khan, Estimation of finite population distribution function in a complex survey sampling Commun. Stat.-Theor. M., 2021, 1–23. https://doi.org/10.1080/03610926.2021.1955386 doi: 10.1080/03610926.2021.1955386
    [16] G. K. Vishwakarma, S. M. Zeeshan, Generalized ratio-cum-product estimator for finite population mean under two-phase sampling scheme, J. Mod. Appl. Stat. Meth., 19 (2021), 7. https://doi.org/10.22237/jmasm/1608553320 doi: 10.22237/jmasm/1608553320
    [17] D. Singh, B. V. Sisodia, S. Nidhi, S. Pundir, Some calibration estimators for finite population mean in two-stage stratified random sampling, Commun. Stat.-Theor. M., 49 (2020), 4234–4247. https://doi.org/10.1080/03610926.2019.1596283 doi: 10.1080/03610926.2019.1596283
    [18] A. Biswas, K. Aditya, U. C. Sud, P. Basak, Product type Calibration estimation of finite population total under two stage sampling, 2020.
    [19] V. I. Salinas, S. A. Sedory, S. Singh, Calibrated estimators in two-stage sampling, Commun. Stat.-Theor. M., 48 (2019), 1449–1469. https://doi.org/10.1080/03610926.2018.1433850 doi: 10.1080/03610926.2018.1433850
    [20] N. K. Bii, C. O. Onyango, J. Odhiambo, Estimating a finite population mean under random non response in two stage cluster sampling with replacement, J. Phys. Conf. Ser., 1132 (2018), 012071. https://doi.org/10.1088/1742-6596/1132/1/012071 doi: 10.1088/1742-6596/1132/1/012071
    [21] S. Ahmad, S. Hussain, S. Ahmad, Finite population distribution function estimation using auxiliary information under simple random sampling, Stat. Comput. Interdisc. Res., 3 (2021), 29–38. https://doi.org/10.52700/scir.v3i1.25 doi: 10.52700/scir.v3i1.25
    [22] J. Shabbir, S. Gupta, Estimation of finite population mean in simple and stratified random sampling using two auxiliary variables, Commun. Stat.-Theor. M., 46 (2017), 10135–10148. https://doi.org/10.1080/03610926.2016.1231822 doi: 10.1080/03610926.2016.1231822
    [23] H. P. Singh, S. Singh, M. Kozak, A family of estimators of finite-population distribution function using auxiliary information, Acta Appl. Math., 104 (2008), 115–130. https://doi.org/10.1007/s10440-008-9243-1 doi: 10.1007/s10440-008-9243-1
    [24] S. K. Yadav, S. Misra, S. S. Mishra, N. Chutiman, Improved ratio estimators of population mean in adaptive cluster sampling, J. Stat. Appl. Probab. Lett., 3 (2016), 1–6.
    [25] S. Al-Marzouki, C. Christophe, S. Akhtar, J. A. Nasir, S. Ahmad, S. Hussain, et al., Estimation of finite population mean under pps in presence of maximum and minimum values, AIMS Math., 6 (2021), 5397–5409. https://doi.org/10.3934/math.2021318 doi: 10.3934/math.2021318
    [26] S. Hussain, S. Ahmad, S. Akhtar, A. Javed, U. Yasmeen, Estimation of finite population distribution function with dual use of auxiliary information under non-response, Plos One, 15 (2020), e0243584. https://doi.org/10.1371/journal.pone.0243584 doi: 10.1371/journal.pone.0243584
    [27] C. Kadilar, H. Cingi, Improvement in estimating the population mean in simple random sampling, Appl. Math. Lett., 19 (2006), 75–79. https://doi.org/10.1016/j.aml.2005.02.039 doi: 10.1016/j.aml.2005.02.039
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(1606) PDF downloads(81) Cited by(6)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(9)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog