In many sampling situations, researchers come across variety of data. These data are largely affected by the parent distribution. There are characteristics which some data share based on the parent distribution. These characteristics define their distribution as well as their behavior. The use of auxiliary variable in estimating a study variable has been on the increase. Auxiliary variable has been used in estimating population means as well as variances. The variance is very sensitive to distribution. Thus, estimating the variance using auxiliary variable might lead to some unexpected results. Hence the need to check the effect of the distribution of the performances of some selected classes of variance estimators. Twelve estimators were selected for comparison. Eight distributions were considered using simulation study. The selected distributions are: Normal, Chi-square, Uniform, Gamma, Exponential, Poisson, Geometric and Binomial. A population size of 330 was used while sample size of 30 was considered using simple random sample without replacement. The estimators were compared using Bias, and Mean Square Error. The performances of the estimators vary in some distributions. The gamma and exponential distributions showed wide variability. The performances of the estimators based on Bias is the same as that based on Mean Square Error. The Mean Square Errors were ranked. The best estimator is t1 followed be t10 and t12. The results showed that the estimators are not distribution free.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 8, Issue 1) |
| DOI | 10.11648/j.sjams.20200801.14 |
| Page(s) | 27-34 |
| 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), 2020. Published by Science Publishing Group |
Mean Square Error, Bias, Estimators, Variance, Parameters, Constants
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APA Style
Etaga Harrison Oghenekevwe, Etaga Cecilia Njideka, Osuoha Chizoba Sylvia. (2020). Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling. Science Journal of Applied Mathematics and Statistics, 8(1), 27-34. https://doi.org/10.11648/j.sjams.20200801.14
ACS Style
Etaga Harrison Oghenekevwe; Etaga Cecilia Njideka; Osuoha Chizoba Sylvia. Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling. Sci. J. Appl. Math. Stat. 2020, 8(1), 27-34. doi: 10.11648/j.sjams.20200801.14
AMA Style
Etaga Harrison Oghenekevwe, Etaga Cecilia Njideka, Osuoha Chizoba Sylvia. Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling. Sci J Appl Math Stat. 2020;8(1):27-34. doi: 10.11648/j.sjams.20200801.14
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Download@article{10.11648/j.sjams.20200801.14,
author = {Etaga Harrison Oghenekevwe and Etaga Cecilia Njideka and Osuoha Chizoba Sylvia},
title = {Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {8},
number = {1},
pages = {27-34},
doi = {10.11648/j.sjams.20200801.14},
url = {https://doi.org/10.11648/j.sjams.20200801.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20200801.14},
abstract = {In many sampling situations, researchers come across variety of data. These data are largely affected by the parent distribution. There are characteristics which some data share based on the parent distribution. These characteristics define their distribution as well as their behavior. The use of auxiliary variable in estimating a study variable has been on the increase. Auxiliary variable has been used in estimating population means as well as variances. The variance is very sensitive to distribution. Thus, estimating the variance using auxiliary variable might lead to some unexpected results. Hence the need to check the effect of the distribution of the performances of some selected classes of variance estimators. Twelve estimators were selected for comparison. Eight distributions were considered using simulation study. The selected distributions are: Normal, Chi-square, Uniform, Gamma, Exponential, Poisson, Geometric and Binomial. A population size of 330 was used while sample size of 30 was considered using simple random sample without replacement. The estimators were compared using Bias, and Mean Square Error. The performances of the estimators vary in some distributions. The gamma and exponential distributions showed wide variability. The performances of the estimators based on Bias is the same as that based on Mean Square Error. The Mean Square Errors were ranked. The best estimator is t1 followed be t10 and t12. The results showed that the estimators are not distribution free.},
year = {2020}
}
TY - JOUR T1 - Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling AU - Etaga Harrison Oghenekevwe AU - Etaga Cecilia Njideka AU - Osuoha Chizoba Sylvia Y1 - 2020/02/20 PY - 2020 N1 - https://doi.org/10.11648/j.sjams.20200801.14 DO - 10.11648/j.sjams.20200801.14 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 - 27 EP - 34 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20200801.14 AB - In many sampling situations, researchers come across variety of data. These data are largely affected by the parent distribution. There are characteristics which some data share based on the parent distribution. These characteristics define their distribution as well as their behavior. The use of auxiliary variable in estimating a study variable has been on the increase. Auxiliary variable has been used in estimating population means as well as variances. The variance is very sensitive to distribution. Thus, estimating the variance using auxiliary variable might lead to some unexpected results. Hence the need to check the effect of the distribution of the performances of some selected classes of variance estimators. Twelve estimators were selected for comparison. Eight distributions were considered using simulation study. The selected distributions are: Normal, Chi-square, Uniform, Gamma, Exponential, Poisson, Geometric and Binomial. A population size of 330 was used while sample size of 30 was considered using simple random sample without replacement. The estimators were compared using Bias, and Mean Square Error. The performances of the estimators vary in some distributions. The gamma and exponential distributions showed wide variability. The performances of the estimators based on Bias is the same as that based on Mean Square Error. The Mean Square Errors were ranked. The best estimator is t1 followed be t10 and t12. The results showed that the estimators are not distribution free. VL - 8 IS - 1 ER -
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