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AIMS Mathematics

2022, Volume 7, Issue 3: 4592-4613. doi: 10.3934/math.2022256
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Research article

Estimation of finite population mean using dual auxiliary variable for non-response using simple random sampling

  • 1.
    Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan
  • 2.
    Department of Statistics, Quaid-i-azam University, Islamabad, Pakistan
  • 3.
    PIDE School of Economics, Pakistan Institute of Development Economics, Islamabad, Pakistan
  • 4.
    Departments of Mathematics, College of Science and Humanities in Al-kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
  • 5.
    Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass, Saudi Arabia
  • Received: 15 July 2021 Revised: 10 December 2021 Accepted: 14 December 2021 Published: 23 December 2021

  • MSC : 65D05

  • This paper addresses the issue of estimating the population mean for non-response using simple random sampling. A new family of estimators is proposed for estimating the population mean with auxiliary information on the sample mean and the rank of the auxiliary variable. Bias and mean square errors of existing and proposed estimators are obtained using the first order of measurement. Theoretical comparisons are made of the performance of the proposed and existing estimators. We show that the proposed family of estimators is more efficient than existing estimators in the literature under the given constraints using these theoretical comparisons.

    Citation: Sohaib Ahmad, Sardar Hussain, Muhammad Aamir, Faridoon Khan, Mohammed N Alshahrani, Mohammed Alqawba. Estimation of finite population mean using dual auxiliary variable for non-response using simple random sampling[J]. AIMS Mathematics, 2022, 7(3): 4592-4613. doi: 10.3934/math.2022256

    Related Papers:

  • This paper addresses the issue of estimating the population mean for non-response using simple random sampling. A new family of estimators is proposed for estimating the population mean with auxiliary information on the sample mean and the rank of the auxiliary variable. Bias and mean square errors of existing and proposed estimators are obtained using the first order of measurement. Theoretical comparisons are made of the performance of the proposed and existing estimators. We show that the proposed family of estimators is more efficient than existing estimators in the literature under the given constraints using these theoretical comparisons.


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    [1] S. Ahmad, S. Hussain, S. Ahmad, Finite population distribution function estimation using auxiliary information under simple random sampling, Stat. Comput. Interdiscip. Res., 3 (2021), 29–38. https://doi.org/10.52700/scir.v3i1.25 doi: 10.52700/scir.v3i1.25
    [2] S. Ahmad, J. Shabbir, Use of extreme values to estimate finite population mean under pps sampling scheme, J. Reliab. Stat. Stud., 11 (2018), 99–112.
    [3] S. Al-Marzouki, C. Chesneau, S. Akhtar, J. N. Abdul, 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
    [4] 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
    [5] W. W. Chanu, B. K. Singh, Improved exponential ratio cum exponential dual to ratio estimator of finite population mean in presence of non-response, J. Stat. Appl. Probab., 4 (2015), 103.
    [6] W. G. Cochran, The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce, J. Agr. Sci., 30 (1940), 262–275. https://doi.org/10.1017/S0021859600048012 doi: 10.1017/S0021859600048012
    [7] W. G. Cochran, G. William, Sampling techniques, New York: John Wiley & Sons, 1977.
    [8] L. K. Grover, P. Kaur, A generalized class of ratio type exponential estimators of population mean under linear transformation of auxiliary variable, Commun. Stat. Simul. Comput., 43 (2014), 1552–1574. https://doi.org/10.1080/03610918.2012.736579 doi: 10.1080/03610918.2012.736579
    [9] D. N. Gujrati, Basic econometrics, Tata McGraw-Hill Education, 2009.
    [10] M. H. Hansen, W. N. Hurwitz, The problem of non-response in sample surveys, J. Amer. Stat. Assoc., 41 (1964), 517–529.
    [11] 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
    [12] 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
    [13] 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 (2020), 1693612. https://doi.org/10.1155/2020/1693612 doi: 10.1155/2020/1693612
    [14] M. Ismail, Combination of ratio and regression estimator of population mean in presence of non–response, Gazi Univ. J. Sci, 30 (2017), 634–642.
    [15] B. B. Khare, S. Kumar, Chain ratio-regression estimators in two phase sampling in the presence of non-response, ProbStat Forum, 8 (2015), 95–102.
    [16] B. B. Khare, R. R. Sinha, Estimation of the ratio of the two population means using multi auxiliary characters in the presence of non-response, In: B. N. Pandey, Statistical techniques in life testing, reliability, sampling theory and quality control, New Delhi: Narosa publishing house, 1 (2007), 63–171.
    [17] B. B. Khare, R. R. Sinha, On class of estimators for population mean using multi-auxiliary characters in the presence of non-response, Stat. Transition, 10 (2009), 3–14.
    [18] B. B. Khare, R. R. Sinha, Estimation of population mean using multi-auxiliary characters with subsampling the nonrespondents, Stat. Transition New Ser., 1 (2011), 45–56.
    [19] B. B. Khare, S. Srivastava, Estimation of population mean using auxiliary character in presence of nonresponse, Natl. Acad. Sci. Lett.-India, 16 (1993), 111–114.
    [20] B. B. Khare, S. Srivastava, Transformed ratio type estimators for the population mean in the presence of nonresponse, Commun. Stat.-Theory M., 26 (1997), 1779–1791. https://doi.org/10.1080/03610929708832012 doi: 10.1080/03610929708832012
    [21] S. Muneer, S. Shabbir, A. Khalil, Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables, Commun. Stat.-Theory M., 46 (2017), 2181–2192. https://doi.org/10.1080/03610926.2015.1035394 doi: 10.1080/03610926.2015.1035394
    [22] M. N. Murthy, Product method of estimation, Sankhya: Indian J. Stat., Ser. A, 26 (1964), 69–74.
    [23] O. Yunusa, S. Kumar, Ratio-cum-product estimator using exponential estimator in the presence of non-response, J. Adv. Comput., 3 (2014), 1–11.
    [24] S. K. Pal, H. P. Singh, Estimation of finite population mean using auxiliary information in presence of non-response, Commun. Stat.-Simul. C., 47 (2018), 143–165. https://doi.org/10.1080/03610918.2017.1280161 doi: 10.1080/03610918.2017.1280161
    [25] P. S. Chami, B. Sing, D. Thomas, A two-parameter ratio-product-ratio estimator in two-phase sampling using auxiliary information in presence of non-response, Int. Scholarly Res. Not., 2012 (2012), 103860. https://doi.org/10.5402/2012/103860 doi: 10.5402/2012/103860
    [26] P. S. R. S. Rao, Ratio estimation with sub sampling the non-respondents, Survey Meth., 12 (1986), 217–230.
    [27] T. J. Rao, On certail methods of improving ration and regression estimators, Commun. Stat.-Theory M., 20 (1991), 3325–3340.
    [28] S. Ahmad, S. Hussain, M. Aamir, U. Yasmeen, J. Shabbir, Z. Ahmad, Dual use of auxiliary information for estimating the finite population mean under the stratified random sampling scheme, J. Math., 2021 (2021), 3860122. https://doi.org/10.1155/2021/3860122 doi: 10.1155/2021/3860122
    [29] R. Singh, P. Chauhan, N. Sawan, F. Smarandache, Improvement in estimating the population mean using exponential estimator in simple random sampling, In: Auxiliary information and a priori values in construction of improved estimators, USA: Renaissance High Press, 2007, 33–40.
    [30] B. Sisodia, V. Dwivedi, Modified ratio estimator using coefficient of variation of auxiliary variable, J. Indian Soc. Agr. Stat., 33 (1981), 13–18.
    [31] M. Yaqub, J. Shabbir, Estimation of population distribution function in the presence of non-response, Hacettepe J. Math. Stat., 47 (2018), 471–511.
    [32] E. Zahid, J. Shabbir, Estimation of population mean in the presence of measurement error and non response under stratified random sampling, PloS One, 13 (2018), e0191572. https://doi.org/10.1371/journal.pone.0191572 doi: 10.1371/journal.pone.0191572
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  • © 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)
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