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Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean

Received: 16 May 2016     Accepted: 26 May 2016     Published: 7 June 2016
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Abstract

In the studies in literature up to date arithmetic population mean of auxiliary variable is used to obtain the proportional estimators. In this paper geometric mean, harmonic mean and quadratic mean is used as well as arithmetic population mean. Using geometric mean, harmonic mean and quadratic mean do not affect the variance of ratio estimator (). However new approaches are obtained for the estimation and variance of the dependent variable when these means are used as well as arithmetic population mean. In the application, the mean number of teaching staff of the departments in Ondokuz Mayıs University is estimated by auxiliary variable which is the number of students in the departments. In addition the variances of proportional estimation method are obtained and interpreted by using population arithmetic mean, geometric mean, harmonic and quadratic mean.

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 3)
DOI 10.11648/j.sjams.20160403.15
Page(s) 115-118
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), 2016. Published by Science Publishing Group

Keywords

Proportional Estimation, Geometric Mean, Harmonic Mean, Quadratic Mean, Inequalities

References
[1] Cochran, W. G., “Sampling Techniques”, John Wiley and Sons, New-York, 1977.
[2] Dayyeh, W. A. A., Ahmed M. S., Ahmed R. A., Mutlak, H. A, “Some estimators of a finite population mean using auxiliary information”, Applied Mathematics and Computation, 139, 287-298, 2003.
[3] Singh, H. P. and Tailor, R., “Use of known correlation coefficient in estimating the finite population mean”, Statistics in Transition, Vol. 6, No. 4, 555-560, 2003.
[4] Ray, S. K. and Singh R. K., “Difference-cum-ratio type estimators, Journal of Indian Statistical Association”, 19, 147- 151, 1981.
[5] Kadılar, C. and Çıngı, H., “Ratio estimators in simple random sampling”, Applied Mathematics and Computation, 151, 893-902, 2004.
[6] Kadılar, C. and Çıngı, H, “A new estimator using two auxiliary variables”, Applied Mathematics and Computation, 162, 901-908, 2005.
[7] Yamane, T., “Temel Örnekleme Yöntemleri, (Çevirinler: Esin, Aydın, C. Bakır, M. A., Gürbüzsel, E.)” Literatür Yayınları, No: 53, İstanbul, 2001.
[8] Shahbazov, A., “Introduction to Probability Theory”, Birsen Yayınevi Ltd. Şti. Kod No: Y. 0029, ISBN: 975-511-415-7, İstanbul, 2005.
[9] Çıngı, H., “Sampling Theory”, H. Ü. Fen Fakültesi Basımevi, Beytepe, 2009.
[10] Isaki, C. T., “Variance estimation using auxiliary information, Journal of American Statistical Assosiation”, 78, 117-123, 1983.
[11] Prasad, B., Singh, H. P., “Unbiased estimators of finite population variance using auxiliary information in sample surveys”, 21, 5, 1367-1376, 1992.
[12] Garcia, M. R., Cebrian, A. A., “Repeated subsitution method: The ratio estimator for the population variance”, Metrika, 43, 101-105, 1996.
[13] Beale, E. M. L., “Some use of computers in operational research, Industrielle Organisation”, 31, 27-28, 1962.
[14] Tin, M., “Comparison of some ratio estimators”, Journal of American Statistical Assosiation, 60, 294-307, 1965.
[15] Zaman, T., Sağlam, V., Sağir, M., Yücesoy, E., and Zobu, M., “Investigation of some estimators Taylor Series approach and an application”, Science Publishing Group, 3 (5): 141-147, 2014.
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    Vedat Sağlam, Tolga Zaman, Erdinç Yücesoy, Murat Sağır. (2016). Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean. Science Journal of Applied Mathematics and Statistics, 4(3), 115-118. https://doi.org/10.11648/j.sjams.20160403.15

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    ACS Style

    Vedat Sağlam; Tolga Zaman; Erdinç Yücesoy; Murat Sağır. Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean. Sci. J. Appl. Math. Stat. 2016, 4(3), 115-118. doi: 10.11648/j.sjams.20160403.15

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    AMA Style

    Vedat Sağlam, Tolga Zaman, Erdinç Yücesoy, Murat Sağır. Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean. Sci J Appl Math Stat. 2016;4(3):115-118. doi: 10.11648/j.sjams.20160403.15

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  • @article{10.11648/j.sjams.20160403.15,
      author = {Vedat Sağlam and Tolga Zaman and Erdinç Yücesoy and Murat Sağır},
      title = {Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {4},
      number = {3},
      pages = {115-118},
      doi = {10.11648/j.sjams.20160403.15},
      url = {https://doi.org/10.11648/j.sjams.20160403.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160403.15},
      abstract = {In the studies in literature up to date arithmetic population mean of auxiliary variable is used to obtain the proportional estimators. In this paper geometric mean, harmonic mean and quadratic mean is used as well as arithmetic population mean. Using geometric mean, harmonic mean and quadratic mean do not affect the variance of ratio estimator (). However new approaches are obtained for the estimation and variance of the dependent variable when these means are used as well as arithmetic population mean. In the application, the mean number of teaching staff of the departments in Ondokuz Mayıs University is estimated by auxiliary variable which is the number of students in the departments. In addition the variances of proportional estimation method are obtained and interpreted by using population arithmetic mean, geometric mean, harmonic and quadratic mean.},
     year = {2016}
    }
    

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  • TY  - JOUR
    T1  - Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean
    AU  - Vedat Sağlam
    AU  - Tolga Zaman
    AU  - Erdinç Yücesoy
    AU  - Murat Sağır
    Y1  - 2016/06/07
    PY  - 2016
    N1  - https://doi.org/10.11648/j.sjams.20160403.15
    DO  - 10.11648/j.sjams.20160403.15
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
    SP  - 115
    EP  - 118
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20160403.15
    AB  - In the studies in literature up to date arithmetic population mean of auxiliary variable is used to obtain the proportional estimators. In this paper geometric mean, harmonic mean and quadratic mean is used as well as arithmetic population mean. Using geometric mean, harmonic mean and quadratic mean do not affect the variance of ratio estimator (). However new approaches are obtained for the estimation and variance of the dependent variable when these means are used as well as arithmetic population mean. In the application, the mean number of teaching staff of the departments in Ondokuz Mayıs University is estimated by auxiliary variable which is the number of students in the departments. In addition the variances of proportional estimation method are obtained and interpreted by using population arithmetic mean, geometric mean, harmonic and quadratic mean.
    VL  - 4
    IS  - 3
    ER  - 

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Author Information
  • Department of Statistics, Faculty of Science and Arts, Ondokuz May?s University, Kurupelit, Turkey

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