Volume 4, Issue 3, June 2016, Page: 115-118
Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean
Vedat Sağlam, Department of Statistics, Faculty of Science and Arts, Ondokuz Mayıs University, Kurupelit, Turkey
Tolga Zaman, Department of Statistics, Faculty of Science and Arts, Ondokuz Mayıs University, Kurupelit, Turkey
Erdinç Yücesoy, Department of Statistics, Faculty of Science and Arts, Ondokuz Mayıs University, Kurupelit, Turkey
Murat Sağır, Department of Statistics, Faculty of Science and Arts, Ondokuz Mayıs University, Kurupelit, Turkey
Received: May 16, 2016;       Accepted: May 26, 2016;       Published: Jun. 7, 2016
DOI: 10.11648/j.sjams.20160403.15      View  2992      Downloads  117
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.
Keywords
Proportional Estimation, Geometric Mean, Harmonic Mean, Quadratic Mean, Inequalities
To cite this article
Vedat Sağlam, Tolga Zaman, Erdinç Yücesoy, Murat Sağır, Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean, Science Journal of Applied Mathematics and Statistics. Vol. 4, No. 3, 2016, pp. 115-118. doi: 10.11648/j.sjams.20160403.15
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[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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