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AIMS Mathematics

2020, Volume 5, Issue 6: 7605-7623. doi: 10.3934/math.2020486
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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.


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  • © 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)
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