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
Volume 6, Issue 6, November 2017, Pages: 270-277
Received: Sep. 17, 2017; Accepted: Oct. 4, 2017; Published: Nov. 10, 2017
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Authors
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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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.
Keywords
Finite Population with Linear Trend, Systematic Sampling, Measurement Errors
To cite this article
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, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 6, 2017, pp. 270-277. doi: 10.11648/j.ajtas.20170606.12
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Copyright © 2017 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.
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