Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 6: 7605-7623. doi: 10.3934/math.2020486
Previous Article Next Article
Research article

Efficient estimation combining exponential and ln functions under two phase sampling

  • 1.
    Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan
  • 2.
    Department of Mathematics and Statistics, California State University, Long Beach, USA
  • 3.
    Department of Mathematics and Statistics, King Abdulaziz University, Jeddah, Saudi Arabia
  • Received: 08 July 2020 Accepted: 14 September 2020 Published: 24 September 2020

  • MSC : 26A33, 42A38

  • In this study, we propose the combination of exponential and ln ratio type estimator to estimate the mean of Y (Study Variable) by incorporating two auxiliary variables in two phase sampling scheme. Under simple random sampling without replacement, the illustration for mean square error and mathematical comparisons are presented. Several approaches are available in literature to estimate the study variable by using information on the variable of interest. The performance of our proposed estimator is compared with other ratio type estimators theoretically and empirically. It is observed that ratio and exponential ratio estimators considered by various researchers and usual unbiased estimator is less efficient than our proposed estimator. An efficiency comparison is also given using five data sets and simulation studies for checking the merits of our proposed estimator and outcomes are sound and moderately illuminating in comparison to different estimators.

    Citation: Yasir Hassan, Muhammad Ismai, Will Murray, Muhammad Qaiser Shahbaz. Efficient estimation combining exponential and ln functions under two phase sampling[J]. AIMS Mathematics, 2020, 5(6): 7605-7623. doi: 10.3934/math.2020486

    Related Papers:

  • In this study, we propose the combination of exponential and ln ratio type estimator to estimate the mean of Y (Study Variable) by incorporating two auxiliary variables in two phase sampling scheme. Under simple random sampling without replacement, the illustration for mean square error and mathematical comparisons are presented. Several approaches are available in literature to estimate the study variable by using information on the variable of interest. The performance of our proposed estimator is compared with other ratio type estimators theoretically and empirically. It is observed that ratio and exponential ratio estimators considered by various researchers and usual unbiased estimator is less efficient than our proposed estimator. An efficiency comparison is also given using five data sets and simulation studies for checking the merits of our proposed estimator and outcomes are sound and moderately illuminating in comparison to different estimators.


    加载中


    [1] J. Velasco-Muñ oz, J. Aznar-Sánchez, L. Belmonte-Ureñ a, et al., Sustainable water use in agriculture: A review of worldwide research, Sustainability, 10 (2018), 1084.
    [2] R. Serbu, B. Marza, S. Borza, A spatial Analytic Hierarchy Process for identification of water pollution with GIS software in an eco-economy environment, Sustainability, 8 (2016), 1208.
    [3] R. Ziemer and W. Tranter, A survey and analysis of electrical engineering curricula in communications and signal processing. IEEE Commun. Mag., 18 (1980), 5-12.
    [4] R. M. De Mello, P. C. Da Silva, G. H. Travassos, Investigating probabilistic sampling approaches for large-scale surveys in software engineering, Journal of Software Engineering Research and Development, 3 (2015), 8.
    [5] R. M. De Mello, G. H. Travassos, Surveys in software engineering: Identifying representative samples, Proceedings of the 10th ACM/IEEE International Symposium on Empirical Software Engineering and Measurement, 2016.
    [6] D. J. Watson, The estimation of leaf area in field crops, J. Agr. Sci, 27 (1937), 474-483.
    [7] 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.
    [8] M. N. Murthy, Product method of estimation, Sankhya, 26 (1964), 294-307.
    [9] D. S. Robson, Applications of multivariate polykays to the theory of unbiased ratio-type estimation, J. Am. Stat. Assoc., 52 (1957), 511-522.
    [10] S. K. Srivastava, A generalized estimator for the mean of a finite population using multi-auxiliary information, J. Am. Stat. Assoc., 66 (1971), 404-407.
    [11] S. Bahl, R. K. Tuteja, Ratio and product type exponential estimators, Journal of information and optimization sciences, 12 (1991), 159-164.
    [12] M. A. Hidiroglou, Double sampling, Survey methodology, 27 (2001), 143-154.
    [13] M. Samiuddin, M. Hanif, Estimation of population mean in single and two phase sampling with or without additional information, Pakistan journal of statistics-all series-, 23 (2007), 99.
    [14] H. P. Singh, M. R. Espejo, Double sampling ratio-product estimator of a finite population mean in sample surveys, J. Appl. Stat., 34 (2007), 71-85.
    [15] H. P. Singh, G. K. Vishwakarma, Modified exponential ratio and product estimators for finite population mean in double sampling, Austrian journal of statistics, 36 (2007), 217-225.
    [16] M. Hanif, N. Hamad, M. Q. Shahbaz, A modified regression type estimator in survey sampling, World Applied Sciences Journal, 7 (2009), 1559-1561.
    [17] M. Hanif, N. Hamad, M. Q. Shahbaz, Some new regression type estimators in two phase sampling, World Applied Sciences Journal, 8 (2010), 799-803.
    [18] H. P. Singh, R. Tailor, R. Tailor, On ratio and product methods with certain known population parameters of auxiliary variable in sample surveys, SORT-Stat Oper. Res. T., 34 (2010), 157-180.
    [19] R. Singh, F. Smarandache, Studies in sampling techniques and time series analysis, Zip publishing, 2011.
    [20] M. Noor-ul-Amin, M. Hanif, SOME EXPONENTIAL ESTIMATORS IN SURVEY SAMPLING, Pakistan Journal of Statistics, 28 (2012).
    [21] R. Tailor, R. Tailor, R. Parmar, et al., Dual to Ratio-cum-Product estimator using known parameters of auxiliary variables, Journal of Reliability and Statistical Studies, 5 (2012), 65-71.
    [22] J. Shabbir, S. Gupta, Z. Hussain, Improved estimation of finite population median under two-phase sampling when using two auxiliary variables, Scientia Iranica, 22 (2015), 1271-1277.
    [23] A. H. Al-Marshadi, A. H. Alharby, M. Q. Shahbaz, On some new estimators of population variance in single and two-phase sampling, Maejo Int. J. Sci. Tech., 12 (2018), 272-281.
    [24] G. K. Vishwakarma, M. Kumar, An improved class of chain ratio-product type estimators in two-phase sampling using two auxiliary variables, Journal of probability and Statistics, 2014.
    [25] G. K. Vishwakarma, M. Kumar, An efficient class of estimators for the mean of a finite population in two-phase sampling using multi-auxiliary variates, Commun. Math. Stat., 3 (2015), 477-489.
    [26] P. R. Dash, G. Mishra, An improved class of estimators in two-phase sampling using two auxiliary variables, Communications in Statistics-Theory and Methods, 40 (2011), 4347-4352.
    [27] P. Mishra, N. K. Adichwal, R. Singh, A New Log-Product-Type Estimator Using Auxiliary Information, Journal of Scientific Research, BHU, Varanasi, 61 (2017), 179-183.
    [28] T. Akhlaq, M. Ismail, M. Q. Shahbaz, On Efficient Estimation of Process Variability, Symmetry, 11 (2019), 554.
    [29] H. P. Singh, G. K. Vishwakarma, Modified exponential ratio and product estimators for finite population mean in double sampling, Austrian journal of statistics, 36 (2007), 217-225.
    [30] W. G. Cochran, Sampling techniques, 3rd Edition, 1977.
    [31] L. Upadhyaya, G. Singh, Chain-type estimators using transformed auxiliary variable in two-phase sampling, ADVANCES IN MODELLING AND ANALYSIS-A-, 38 (2001), 1a-10a.
    [32] R. Singh, M. Kumar, F. Smarandache, ALMOST UNBIASED ESTIMATOR FOR ESTIMATING POPULATION MEAN USING KNOWN VALUE OF SOME POPULATION PARAMETER(S), Pakistan Journal of Statistics and Operation Research, 4 (2008), 63-76.
    [33] A. Sanaullah, H. Khan, H. A. Ali, et al., Improved exponential ratio-type estimators in survey sampling, Journal of Reliability and Statistical Studies, 5 (2012), 119-132.
    [34] C. Kadilar, H. Cingi, A new estimator using two auxiliary variables, Appl. Math. Comput., 162 (2005), 901-908.
    [35] H. O. Cekim, C. Kadilar, In-type estimators for the population variance in stratified random sampling, Communications in Statistics-Simulation and Computation, 49 (2020), 1665-1677.
    [36] S. Bandyopadhyay, Improved ratio and product estimators, Sankhya, 42 (1980), 45-49.
    [37] T. Srivenkataramana, A dual to ratio estimator in sample surveys, Biometrika, 67 (1980), 199-204.
  • Reader Comments
  • © 2020 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(3300) PDF downloads(217) Cited by(4)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(4)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog