Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme
In this paper, we proposed an improved family of estimators for finite population mean under stratified random sampling, which needed a helping variable on the sample mean and rank of the auxiliary variable. The expression of the bias and mean square error of the proposed and existing estimators are...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/3860122 |
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| _version_ | 1832563458951872512 |
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| author | Sohaib Ahmad Sardar Hussain Muhammad Aamir Uzma Yasmeen Javid Shabbir Zubair Ahmad |
| author_facet | Sohaib Ahmad Sardar Hussain Muhammad Aamir Uzma Yasmeen Javid Shabbir Zubair Ahmad |
| author_sort | Sohaib Ahmad |
| collection | DOAJ |
| description | In this paper, we proposed an improved family of estimators for finite population mean under stratified random sampling, which needed a helping variable on the sample mean and rank of the auxiliary variable. The expression of the bias and mean square error of the proposed and existing estimators are computed up to the first-order approximation. The estimators proposed in different situations were investigated and provided a minimum mean square error relative to all other estimators considered. Four actual data sets and simulation studies are carried out to observe the performance of the estimators. For simulation study, R software is used. The mean square errors of all four data sets are minimum and percent relative efficiencies are more than a hundred percent higher than the other existing estimators, which indicated the importance of the newly proposed family of estimators. From the simulation study, it is concluded that the suggested family of estimators achieved better results. We demonstrate theoretically and numerically that the proposed estimator produces efficient results compared to all other contend estimators in entire situations. Overall, we conclude that the performance of the family of suggested estimators is better than all existing estimators. |
| format | Article |
| id | doaj-art-dc2f338cd00f424fa1b7c31ae7f72bec |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-dc2f338cd00f424fa1b7c31ae7f72bec2025-02-03T01:20:13ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/3860122Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling SchemeSohaib Ahmad0Sardar Hussain1Muhammad Aamir2Uzma Yasmeen3Javid Shabbir4Zubair Ahmad5Department of StatisticsDepartment of StatisticsDepartment of StatisticsInstitute of Molecular Biology and BiotechnologyDepartment of StatisticsDepartment of StatisticsIn this paper, we proposed an improved family of estimators for finite population mean under stratified random sampling, which needed a helping variable on the sample mean and rank of the auxiliary variable. The expression of the bias and mean square error of the proposed and existing estimators are computed up to the first-order approximation. The estimators proposed in different situations were investigated and provided a minimum mean square error relative to all other estimators considered. Four actual data sets and simulation studies are carried out to observe the performance of the estimators. For simulation study, R software is used. The mean square errors of all four data sets are minimum and percent relative efficiencies are more than a hundred percent higher than the other existing estimators, which indicated the importance of the newly proposed family of estimators. From the simulation study, it is concluded that the suggested family of estimators achieved better results. We demonstrate theoretically and numerically that the proposed estimator produces efficient results compared to all other contend estimators in entire situations. Overall, we conclude that the performance of the family of suggested estimators is better than all existing estimators.http://dx.doi.org/10.1155/2021/3860122 |
| spellingShingle | Sohaib Ahmad Sardar Hussain Muhammad Aamir Uzma Yasmeen Javid Shabbir Zubair Ahmad Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme Journal of Mathematics |
| title | Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme |
| title_full | Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme |
| title_fullStr | Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme |
| title_full_unstemmed | Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme |
| title_short | Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme |
| title_sort | dual use of auxiliary information for estimating the finite population mean under the stratified random sampling scheme |
| url | http://dx.doi.org/10.1155/2021/3860122 |
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