This paper considers the problem of estimating the population mean in Simple Random Sampling. One key objective of any statistical estimation process is to find estimates of parameter of interest with more efficiency. It is well established that incorporating additional information in the estimation procedure gives enhanced estimators. Ratio estimation improves accuracy of the estimate of the population mean by incorporating prior information of a supporting variable that is highly associated with the main variable. This paper incorporates non-conventional measure (Tri-mean) with quartile deviation as they are not affected by outliers together with kurtosis coefficients and information on the sample size to develop an estimator with more precision. Using Taylor series expansion, the properties of the estimator are evaluated to first degree order. Further, the estimator’s properties are assessed by bias and mean squared error. Efficiency conditions are derived theoretically whereby the suggested estimator performs better than the prevailing estimators. To support the theoretical results, simulation and numerical studies are undertaken to assess efficiency of the suggested estimator over the existing estimators. Empirical analysis done through percentage relative efficiency indicate the suggested estimator performs better compared to the prevailing estimators. It is concluded that the suggested estimator is more efficient than the existing estimators.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 11, Issue 6) |
| DOI | 10.11648/j.ajtas.20221106.11 |
| Page(s) | 167-174 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Ratio Estimator, Non-conventional Location Parameters, Auxiliary Information, Mean Squared Error
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APA Style
Sheryl Chebet Kosgey, Leo Odongo. (2022). Ratio Estimator of Population Mean in Simple Random Sampling. American Journal of Theoretical and Applied Statistics, 11(6), 167-174. https://doi.org/10.11648/j.ajtas.20221106.11
ACS Style
Sheryl Chebet Kosgey; Leo Odongo. Ratio Estimator of Population Mean in Simple Random Sampling. Am. J. Theor. Appl. Stat. 2022, 11(6), 167-174. doi: 10.11648/j.ajtas.20221106.11
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Download@article{10.11648/j.ajtas.20221106.11,
author = {Sheryl Chebet Kosgey and Leo Odongo},
title = {Ratio Estimator of Population Mean in Simple Random Sampling},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {11},
number = {6},
pages = {167-174},
doi = {10.11648/j.ajtas.20221106.11},
url = {https://doi.org/10.11648/j.ajtas.20221106.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221106.11},
abstract = {This paper considers the problem of estimating the population mean in Simple Random Sampling. One key objective of any statistical estimation process is to find estimates of parameter of interest with more efficiency. It is well established that incorporating additional information in the estimation procedure gives enhanced estimators. Ratio estimation improves accuracy of the estimate of the population mean by incorporating prior information of a supporting variable that is highly associated with the main variable. This paper incorporates non-conventional measure (Tri-mean) with quartile deviation as they are not affected by outliers together with kurtosis coefficients and information on the sample size to develop an estimator with more precision. Using Taylor series expansion, the properties of the estimator are evaluated to first degree order. Further, the estimator’s properties are assessed by bias and mean squared error. Efficiency conditions are derived theoretically whereby the suggested estimator performs better than the prevailing estimators. To support the theoretical results, simulation and numerical studies are undertaken to assess efficiency of the suggested estimator over the existing estimators. Empirical analysis done through percentage relative efficiency indicate the suggested estimator performs better compared to the prevailing estimators. It is concluded that the suggested estimator is more efficient than the existing estimators.},
year = {2022}
}
TY - JOUR T1 - Ratio Estimator of Population Mean in Simple Random Sampling AU - Sheryl Chebet Kosgey AU - Leo Odongo Y1 - 2022/11/04 PY - 2022 N1 - https://doi.org/10.11648/j.ajtas.20221106.11 DO - 10.11648/j.ajtas.20221106.11 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 167 EP - 174 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20221106.11 AB - This paper considers the problem of estimating the population mean in Simple Random Sampling. One key objective of any statistical estimation process is to find estimates of parameter of interest with more efficiency. It is well established that incorporating additional information in the estimation procedure gives enhanced estimators. Ratio estimation improves accuracy of the estimate of the population mean by incorporating prior information of a supporting variable that is highly associated with the main variable. This paper incorporates non-conventional measure (Tri-mean) with quartile deviation as they are not affected by outliers together with kurtosis coefficients and information on the sample size to develop an estimator with more precision. Using Taylor series expansion, the properties of the estimator are evaluated to first degree order. Further, the estimator’s properties are assessed by bias and mean squared error. Efficiency conditions are derived theoretically whereby the suggested estimator performs better than the prevailing estimators. To support the theoretical results, simulation and numerical studies are undertaken to assess efficiency of the suggested estimator over the existing estimators. Empirical analysis done through percentage relative efficiency indicate the suggested estimator performs better compared to the prevailing estimators. It is concluded that the suggested estimator is more efficient than the existing estimators. VL - 11 IS - 6 ER -
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