Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean

Vedat Sağlam; Tolga Zaman; Erdinç Yücesoy; Murat Sağır

doi:doi:10.11648/j.sjams.20160403.15

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Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean

Vedat Sağlam, Tolga Zaman, Erdinç Yücesoy, Murat Sağır

Published in Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 3)

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

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[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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APA Style

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

Vedat Sağlam
Tolga Zaman

Department of Statistics, Faculty of Science and Arts, Ondokuz May?s University, Kurupelit, Turkey
Erdinç Yücesoy
Murat Sağır

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APA Style

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download