Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling

Oloo Odhiambo Erick; James Kahiri; Wafula Mike Erick

doi:doi:10.11648/j.ajtas.20170606.12

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Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling

Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)

Received: 17 September 2017 Accepted: 4 October 2017 Published: 10 November 2017

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Abstract

The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.

Published in	American Journal of Theoretical and Applied Statistics (Volume 6, Issue 6)
DOI	10.11648/j.ajtas.20170606.12
Page(s)	270-277
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), 2017. Published by Science Publishing Group

Keywords

Finite Population with Linear Trend, Systematic Sampling, Measurement Errors

References

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[7]	Conor, G., Temblay, M., Moher, D., and Gorver, B. (2007). A comparison of Direct vs Self-reported Measures for Assessing Height, Weight and Body Mass Index: a systematic review. Obesity Rev. 8:307-326.
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APA Style

Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick. (2017). Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. American Journal of Theoretical and Applied Statistics, 6(6), 270-277. https://doi.org/10.11648/j.ajtas.20170606.12

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ACS Style

Oloo Odhiambo Erick; James Kahiri; Wafula Mike Erick. Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. Am. J. Theor. Appl. Stat. 2017, 6(6), 270-277. doi: 10.11648/j.ajtas.20170606.12

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AMA Style

Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick. Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. Am J Theor Appl Stat. 2017;6(6):270-277. doi: 10.11648/j.ajtas.20170606.12

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@article{10.11648/j.ajtas.20170606.12,
  author = {Oloo Odhiambo Erick and James Kahiri and Wafula Mike Erick},
  title = {Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {6},
  pages = {270-277},
  doi = {10.11648/j.ajtas.20170606.12},
  url = {https://doi.org/10.11648/j.ajtas.20170606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170606.12},
  abstract = {The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.},
 year = {2017}
}

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TY  - JOUR
T1  - Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling
AU  - Oloo Odhiambo Erick
AU  - James Kahiri
AU  - Wafula Mike Erick
Y1  - 2017/11/10
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.12
DO  - 10.11648/j.ajtas.20170606.12
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  - 270
EP  - 277
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170606.12
AB  - The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.
VL  - 6
IS  - 6
ER  -

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Author Information

Oloo Odhiambo Erick

Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
James Kahiri

Department of Statistics and Actuarial Science, Kenyatta University (KU), Nairobi, Kenya
Wafula Mike Erick

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

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Plain Text BibTeX RIS

APA Style

Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick. (2017). Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. American Journal of Theoretical and Applied Statistics, 6(6), 270-277. https://doi.org/10.11648/j.ajtas.20170606.12

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ACS Style

Oloo Odhiambo Erick; James Kahiri; Wafula Mike Erick. Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. Am. J. Theor. Appl. Stat. 2017, 6(6), 270-277. doi: 10.11648/j.ajtas.20170606.12

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AMA Style

Oloo Odhiambo Erick, James Kahiri, Wafula Mike Erick. Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling. Am J Theor Appl Stat. 2017;6(6):270-277. doi: 10.11648/j.ajtas.20170606.12

Copy | Download

@article{10.11648/j.ajtas.20170606.12,
  author = {Oloo Odhiambo Erick and James Kahiri and Wafula Mike Erick},
  title = {Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {6},
  number = {6},
  pages = {270-277},
  doi = {10.11648/j.ajtas.20170606.12},
  url = {https://doi.org/10.11648/j.ajtas.20170606.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170606.12},
  abstract = {The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Impact of Measurement Errors on Estimators of Parameters of a Finite Population with Linear Trend Under Systematic Sampling
AU  - Oloo Odhiambo Erick
AU  - James Kahiri
AU  - Wafula Mike Erick
Y1  - 2017/11/10
PY  - 2017
N1  - https://doi.org/10.11648/j.ajtas.20170606.12
DO  - 10.11648/j.ajtas.20170606.12
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  - 270
EP  - 277
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20170606.12
AB  - The study involves investigating the impact of measurement errors on estimators of parameters of a finite population with linear trend among population values, under systematic sampling. The study provides deep understanding on the amount and nature of deviation introduced by errors and how these errors affect estimators of parameters of a population with linear trend. Consideration is given to measurement errors that assume a normal distribution. Systematic sampling technique is used where a sample of size n is selected randomly from a finite population with a fixed interval a. Systematic sampling is considered instead of simple random sampling in this case because of its effectiveness in dealing with linear trend. The explicit values of population totals, means and variances together with their estimates are derived. The results indicate that there can be overestimate of the population mean if the expected systematic errors tend towards positive values and underestimate if the expected systematic error tend towards negative values. When random errors are considered, there is no effect on estimated population parameters.
VL  - 6
IS  - 6
ER  -

Copy | Download