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Ratio Estimator of Population Mean in Simple Random Sampling

Received: 9 October 2022     Accepted: 27 October 2022     Published: 4 November 2022
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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.

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), 2022. Published by Science Publishing Group

Keywords

Ratio Estimator, Non-conventional Location Parameters, Auxiliary Information, Mean Squared Error

References
[1] Abid, M., Abbas, N., Nazir, H. Z. and Lin, Z. (2016). Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters. Revista Colombiana de Estadística, 39 (1), 63-79.
[2] Cochran, W. G. (1940). The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. The Journal of Agricultural Science, 30 (2), 262-275.
[3] Robson, D. S. (1957). Applications of Multivariate Polykays to the Theory of Unbiased Ratio-Type Estimation. Journal of the American Statistical Association, 52 (280), 511–522.
[4] Jeelani, M. I. and Maqbool, S. (2013). Modified ratio estimators of population mean using linear combination of co-efficient of skewness and quartile deviation. The South Pacific Journal of Natural and Applied Sciences, 31 (1), 39.
[5] Kadilar, C. and Cingi, H. (2006). Improvement in estimating the population mean in simple random sampling. Applied Mathematics Letters, 19 (1), 75-79.
[6] Shittu, O. I. and Adepoju, K. A. (2014). On the efficiency of modified ratio estimator based on linear combination of kurtosis, median and quartile deviation. International Journal of Modern Mathematical Sciences, Vol. 103-107.
[7] Singh, H. P. and Tailor, R. (2003). Use of known correlation co-efficient in estimating the finite population means. Statistics in Transition, pp. 555-560.
[8] Srivenkataramana, T. and Tracy, D. S. (1979). On ratio and product methods of estimation in sampling. Statistica Neerlandica, 33 (1), 37-49.
[9] Subramani, J. and Kumarapandiyan, G. (2012). Estimation of Population Mean Using Known Median and Co-Efficent of Skewness. American Journal of Mathematics and Statistics, 2 (5), 101-107.
[10] Subzar M, Maqbool S, Raja TA, Mir SA, Jeelani MI, Bhat MA (2018) Improved family of ratio type estimators for estimating population mean using conventional and non-conventional location parameters. Investigación Operacional, 38 (5): 510-524.
[11] Upadhyaya, L. N. and Singh, H. P. (1999). Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean. Biometrical Journal, 41 (5), 627-636.
[12] Wolter, K. M. (1985). Introduction to Variance Estimation, (Springer-Verlag).
[13] Yadav, S. K., & Zaman, T. (2021). Use of some conventional and non-conventional parameters for improving the efficiency of ratio-type estimators. Journal of Statistics and Management Systems, 1–24.
[14] Yan, Z. and Tian, B. (2010). Ratio Method to the Mean Estimation Using Coefficient of Skewness of Auxiliary Variable. Communications in Computer and Information Science, 103-11.
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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

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    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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    AMA 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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  • @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}
    }
    

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  • 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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Author Information
  • Department of Mathematics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

  • Department of Mathematics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya

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