Science Journal of Applied Mathematics and Statistics

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Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling

Received: 29 January 2020    Accepted: 12 February 2020    Published: 20 February 2020
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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.

DOI 10.11648/j.sjams.20200801.14
Published in Science Journal of Applied Mathematics and Statistics (Volume 8, Issue 1, February 2020)
Page(s) 27-34
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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), 2024. Published by Science Publishing Group

Keywords

Mean Square Error, Bias, Estimators, Variance, Parameters, Constants

References
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Author Information
  • Department of Statistics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

  • Department of Statistics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

  • Department of Statistics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria

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    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

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    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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    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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  • @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://download.sciencepg.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}
    }
    

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    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
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    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
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    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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