Investigation of Some Estimators Via Taylor Series Approach and an Application

Tolga Zaman; Vedat Saglam; Murat Sagir; Erdinc Yucesoy; Mujgan Zobu

doi:doi:10.11648/j.ajtas.20140305.14

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Investigation of Some Estimators Via Taylor Series Approach and an Application

Tolga Zaman, Vedat Saglam, Murat Sagir, Erdinc Yucesoy, Mujgan Zobu

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 5)

Received: 1 September 2014 Accepted: 12 September 2014 Published: 20 September 2014

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Abstract

In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.

Published in	American Journal of Theoretical and Applied Statistics (Volume 3, Issue 5)
DOI	10.11648/j.ajtas.20140305.14
Page(s)	141-147
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), 2014. Published by Science Publishing Group

Keywords

Simple Random Sampling, Taylor Series Approach, Mean, Proportional Estimators, Mean Square Error, Units Ratio having Certain Features, Ancillary Information

References

[1]	Pawliszyn, Janusz., 2012. Comprehensive Sampling and Sample Preparation, 1-30.
[2]	Cochran, W. G., 1977. Sampling Techniques, John Wiley and Sons, New-York.
[3]	Singh, H. P.,Tailor, R., 2003. Use of Known Correlation Coefficient in Estimating the Finite Population Mean, Statistics in Transition, 6, 555-560.
[4]	Ray, S. K.,Singh, R. K., 1981. Difference-cum-ratio type estimators, J. Ind. Statist. Assoc., 19, 147-151.
[5]	Kadılar, C., Çıngı H., 2004. Ratio Estimators in Simple Random Sampling, Applied Mathematics and Computation, 151, 893-902.
[6]	Kadılar, C., Çıngı, H., 2006. New Ratio Estimators Using Correlation Coefficient, İnterstat 4, pp, 1-11.
[7]	Naik, 6., V. D., Gupta, P. C., 1996. A note on estimation of mean with known population proportion of an auxiliary character. Jour. Ind. Soc. Agr. Stat., 48(2), 151-158.
[8]	Singh, R., Chauhan, P., Sawan, N., Smarandache, F., 2008. Ratio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute, Pak. j. stat. oper. res. Vol.IV No. 1 2008.
[9]	Number of teachers and students in Secondary Schools, 2012. Trabzon Provincial Directorate of National Education.
[10]	Çıngı, H., 2009. Örnekleme Kuramı, H.Ü. Fen Fakültesi Basımevi, Beytepe.

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APA Style

Tolga Zaman, Vedat Saglam, Murat Sagir, Erdinc Yucesoy, Mujgan Zobu. (2014). Investigation of Some Estimators Via Taylor Series Approach and an Application. American Journal of Theoretical and Applied Statistics, 3(5), 141-147. https://doi.org/10.11648/j.ajtas.20140305.14

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ACS Style

Tolga Zaman; Vedat Saglam; Murat Sagir; Erdinc Yucesoy; Mujgan Zobu. Investigation of Some Estimators Via Taylor Series Approach and an Application. Am. J. Theor. Appl. Stat. 2014, 3(5), 141-147. doi: 10.11648/j.ajtas.20140305.14

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AMA Style

Tolga Zaman, Vedat Saglam, Murat Sagir, Erdinc Yucesoy, Mujgan Zobu. Investigation of Some Estimators Via Taylor Series Approach and an Application. Am J Theor Appl Stat. 2014;3(5):141-147. doi: 10.11648/j.ajtas.20140305.14

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@article{10.11648/j.ajtas.20140305.14,
  author = {Tolga Zaman and Vedat Saglam and Murat Sagir and Erdinc Yucesoy and Mujgan Zobu},
  title = {Investigation of Some Estimators Via Taylor Series Approach and an Application},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {5},
  pages = {141-147},
  doi = {10.11648/j.ajtas.20140305.14},
  url = {https://doi.org/10.11648/j.ajtas.20140305.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140305.14},
  abstract = {In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.},
 year = {2014}
}

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TY  - JOUR
T1  - Investigation of Some Estimators Via Taylor Series Approach and an Application
AU  - Tolga Zaman
AU  - Vedat Saglam
AU  - Murat Sagir
AU  - Erdinc Yucesoy
AU  - Mujgan Zobu
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140305.14
DO  - 10.11648/j.ajtas.20140305.14
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  - 141
EP  - 147
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140305.14
AB  - In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.
VL  - 3
IS  - 5
ER  -

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Author Information

Tolga Zaman

Department of Statistics, Faculty of Science and Arts, OndokuzMay?s University, Kurupelit, Turkey
Vedat Saglam

Department of Statistics, Faculty of Science and Arts, OndokuzMay?s University, Kurupelit, Turkey
Murat Sagir

Department of Statistics, Faculty of Science and Arts, OndokuzMay?s University, Kurupelit, Turkey
Erdinc Yucesoy

Department of Statistics, Faculty of Science and Arts, OndokuzMay?s University, Kurupelit, Turkey
Mujgan Zobu

Department of Statistics, Faculty of Science and Arts, Amasya University, Turkey

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APA Style

Tolga Zaman, Vedat Saglam, Murat Sagir, Erdinc Yucesoy, Mujgan Zobu. (2014). Investigation of Some Estimators Via Taylor Series Approach and an Application. American Journal of Theoretical and Applied Statistics, 3(5), 141-147. https://doi.org/10.11648/j.ajtas.20140305.14

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ACS Style

Tolga Zaman; Vedat Saglam; Murat Sagir; Erdinc Yucesoy; Mujgan Zobu. Investigation of Some Estimators Via Taylor Series Approach and an Application. Am. J. Theor. Appl. Stat. 2014, 3(5), 141-147. doi: 10.11648/j.ajtas.20140305.14

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AMA Style

Tolga Zaman, Vedat Saglam, Murat Sagir, Erdinc Yucesoy, Mujgan Zobu. Investigation of Some Estimators Via Taylor Series Approach and an Application. Am J Theor Appl Stat. 2014;3(5):141-147. doi: 10.11648/j.ajtas.20140305.14

Copy | Download

@article{10.11648/j.ajtas.20140305.14,
  author = {Tolga Zaman and Vedat Saglam and Murat Sagir and Erdinc Yucesoy and Mujgan Zobu},
  title = {Investigation of Some Estimators Via Taylor Series Approach and an Application},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {5},
  pages = {141-147},
  doi = {10.11648/j.ajtas.20140305.14},
  url = {https://doi.org/10.11648/j.ajtas.20140305.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140305.14},
  abstract = {In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Investigation of Some Estimators Via Taylor Series Approach and an Application
AU  - Tolga Zaman
AU  - Vedat Saglam
AU  - Murat Sagir
AU  - Erdinc Yucesoy
AU  - Mujgan Zobu
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140305.14
DO  - 10.11648/j.ajtas.20140305.14
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  - 141
EP  - 147
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140305.14
AB  - In this study, the use of taylor series method in the calculation of some means with single auxiliary variable developed in a simple random sampling and mean square error unit ratio estimators having certain properties was investigated. An application was performed in respect thereof. The study population (mass) included 111 secondary schools from 18 districts of Trabzon province. Auxiliary variable (x) was taken as the number of students whereas the main variable (y) was taken as the number of teachers. Sample size was calculated as 45 for unit ratio that has certain features. Afterwards, theoretically proposed mean and units ratio estimators having certain properties were compared numerically. Random sampling was performed using the SPSS 20 program thus giving an equal chance to the units sampled and variability in the population was protected.
VL  - 3
IS  - 5
ER  -

Copy | Download