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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Autores principales:	Sohaib Ahmad, Sardar Hussain, Muhammad Aamir, Uzma Yasmeen, Javid Shabbir, Zubair Ahmad
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/dc2f338cd00f424fa1b7c31ae7f72bec
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spelling	oai:doaj.org-article:dc2f338cd00f424fa1b7c31ae7f72bec2021-11-29T00:55:42ZDual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme2314-478510.1155/2021/3860122https://doaj.org/article/dc2f338cd00f424fa1b7c31ae7f72bec2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/3860122https://doaj.org/toc/2314-4785In 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.Sohaib AhmadSardar HussainMuhammad AamirUzma YasmeenJavid ShabbirZubair AhmadHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 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
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
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
title	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_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_sort	dual use of auxiliary information for estimating the finite population mean under the stratified random sampling scheme
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/dc2f338cd00f424fa1b7c31ae7f72bec
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Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme

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