Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming
In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/686579 |
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| _version_ | 1832555260225257472 |
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| author | Atta Ullah Javid Shabbir Zawar Hussain Bander Al-Zahrani |
| author_facet | Atta Ullah Javid Shabbir Zawar Hussain Bander Al-Zahrani |
| author_sort | Atta Ullah |
| collection | DOAJ |
| description | In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real life situations, a linear cost function of a sample size nh is not a good approximation to actual cost of sample survey when traveling cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling with proposed cost function is formulated in integer nonlinear multiobjective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of proposed compromise allocation. |
| format | Article |
| id | doaj-art-200d793dc35747cba00465263457c357 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-200d793dc35747cba00465263457c3572025-02-03T05:48:38ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/686579686579Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal ProgrammingAtta Ullah0Javid Shabbir1Zawar Hussain2Bander Al-Zahrani3Department of Mathematics, Comsats Institute of Information Technology, Attock 43600, PakistanDepartment of Statistics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Statistics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Statistics, King Abdulaziz University, Jeddah 21589, Saudi ArabiaIn practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real life situations, a linear cost function of a sample size nh is not a good approximation to actual cost of sample survey when traveling cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling with proposed cost function is formulated in integer nonlinear multiobjective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of proposed compromise allocation.http://dx.doi.org/10.1155/2014/686579 |
| spellingShingle | Atta Ullah Javid Shabbir Zawar Hussain Bander Al-Zahrani Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming Journal of Applied Mathematics |
| title | Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming |
| title_full | Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming |
| title_fullStr | Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming |
| title_full_unstemmed | Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming |
| title_short | Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming |
| title_sort | estimation of finite population mean in multivariate stratified sampling under cost function using goal programming |
| url | http://dx.doi.org/10.1155/2014/686579 |
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