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Sher K, Ameeq M, Hassan MM, Albalawi O, Afzal A. Development of improved estimators of finite population mean in simple random sampling with dual auxiliaries and its application to real world problems. Heliyon 2024; 10:e30991. [PMID: 38778985 PMCID: PMC11109797 DOI: 10.1016/j.heliyon.2024.e30991] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2024] [Revised: 05/02/2024] [Accepted: 05/09/2024] [Indexed: 05/25/2024] Open
Abstract
In general, the incorporation of supplementary information reduces the Mean Square Error (MSE) and, consequently, enhances the precision of estimating a population parameter. This improvement relies on the appropriate application of a suitable function, with careful consideration. This study introduces two innovative families of estimators for the finite population mean, both of which exhibit superior performance in scenarios involving dual auxiliary information in simple random sampling. Expressions up to the first-order approximation, for bias, and Mean Square Error were derived, and the conditions under which these proposed families surpassed the existing estimators. Our evaluation involved the use of both real and simulated data to compute the Mean Square Error and Percent Relative Efficiency (PRE) of the estimators. A comparative analysis revealed that under the specified conditions, both proposed families yielded more precise results.
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Affiliation(s)
- Khazan Sher
- Department of Statistics University of Peshawar, Pakistan
| | - Muhammad Ameeq
- Department of Statistics, The Islamia University Bahawalpur, Punjab, Pakistan
| | | | - Olayan Albalawi
- Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
| | - Ayesha Afzal
- Department of Computer Science, Air University, Islamabad, Pakistan
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Ahmad S, Shabbir J, Emam W, Zahid E, Aamir M, Khalid M, Muhammad Anas M. An improved class of estimators for estimation of population distribution functions under stratified random sampling. Heliyon 2024; 10:e28272. [PMID: 38560211 PMCID: PMC10979068 DOI: 10.1016/j.heliyon.2024.e28272] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2023] [Revised: 03/06/2024] [Accepted: 03/14/2024] [Indexed: 04/04/2024] Open
Abstract
The main objective of the current study is to suggest an enhanced family of log ratio-exponential type estimators for population distribution function (DF) using auxiliary information under stratified random sampling. Putting different choices in our suggested generalized class of estimators, we found some Specific estimators. The bias and MSE expressions of the estimators have been approximated up to the first order. By using the actual and simulated data sets, we measured the performance of estimators. Based on the results, the suggested estimators for DF show better performance as compared to the preliminary estimators considered here. The suggested estimators have a advanced efficiency than the other estimators examined with the estimators F ‾ ˆ l o g P R ( s t ) 2 , and F ‾ ˆ l o g P R ( s t ) 4 for both the actual and simulated data sets. The magnitude of the improvement in efficiency is noteworthy, indicating the superiority of the proposed estimators in terms of MSE.
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Affiliation(s)
- Sohaib Ahmad
- Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan
| | - Javid Shabbir
- Department of Statistics, University of Wah, Wah Cantt, Pakistan
| | - Walid Emam
- Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia
| | - Erum Zahid
- Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan
| | - Muhammad Aamir
- Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan
| | - Mohd Khalid
- Department of Statistics, Aligarh Muslim University, Aligarh, India
| | - Malik Muhammad Anas
- Department of Economics and Statistics, University of Salerno, Fisciano (Salerno) 84084, Italy
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Pandey MK, Singh GN, Zaman T, Mutairi AA, Mustafa MS. A general class of improved population variance estimators under non-sampling errors using calibrated weights in stratified sampling. Sci Rep 2024; 14:2948. [PMID: 38316812 PMCID: PMC10844305 DOI: 10.1038/s41598-023-47234-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 11/10/2023] [Indexed: 02/07/2024] Open
Abstract
This paper proposes a new calibration estimator for population variance within a stratified two-phase sampling design. It takes into account random non-response and measurement errors, specifically applying this method to estimate the variance in Gas turbine exhaust pressure data. The study integrates additional information from two highly positively correlated auxiliary variables to develop a general class of estimators tailored for the stratified two-phase sampling scheme. The properties of these estimators, in terms of their biases and mean square errors, have been thoroughly examined and extensively analyzed through numerical and simulation studies. Furthermore, the calibrated weights of the strata are derived. The proposed estimators outperform the natural estimator of population variance. Finally, suitable recommendations have been made for survey statisticians intending to apply these findings to real-life problems.
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Affiliation(s)
- M K Pandey
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India.
| | - G N Singh
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India
| | - Tolga Zaman
- Faculty of Health Sciences, Gumushane University, Gumushane, Turkey
| | - Aned Al Mutairi
- Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
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Ahmad S, Hussain S, Al Mutairi A, Kamal M, Rehman MU, SidAhmed Mustafa M. Improved estimation of population distribution function using twofold auxiliary information under simple random sampling. Heliyon 2024; 10:e24115. [PMID: 38298620 PMCID: PMC10828653 DOI: 10.1016/j.heliyon.2024.e24115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2023] [Revised: 12/23/2023] [Accepted: 01/03/2024] [Indexed: 02/02/2024] Open
Abstract
In this article, our main aim is to suggest enhanced families of estimators for estimating the population distribution function (DF) using twofold auxiliary evidence within the framework of simple random sampling. Numerical analysis is performed on four different actual data sets. The precision of the estimators is further investigated exhausting a simulation study. As equated with existing estimators, the suggested families of estimators have minimum mean square error (MSE) and higher percentage relative efficiency (PRE). The succeeding recommended family of estimators outperforms the first family of estimators across all data sets. These are positive indicators of its performance. The theoretical result shows that the recommended family of estimators performs better than the existing estimators. The extent of improvement in efficiency is noteworthy, indicating the superiority of the suggested estimators in terms of minimum MSE.
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Affiliation(s)
- Sohaib Ahmad
- Department of Statistics, Abdul Wali Khan University, Mardan, Pakistan
| | - Sardar Hussain
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Aned Al Mutairi
- Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O Box 84428, Riyadh, 11671, Saudi Arabia
| | - Mustafa Kamal
- Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Dammam, 23356, Saudi Arabia
| | - Masood Ur Rehman
- Department of Information Technology, College of Computing and Informatics, Saudi Electronic University, Dammam, 32256, Saudi Arabia
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Singh HP, Gupta A, Tailor R. Efficient class of estimators for finite population mean using auxiliary attribute in stratified random sampling. Sci Rep 2023; 13:10253. [PMID: 37355677 DOI: 10.1038/s41598-023-34603-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 05/04/2023] [Indexed: 06/26/2023] Open
Abstract
The aim of this paper is to develop more effective methods for estimating population means in sample surveys using auxiliary attributes. To achieve this goal, we introduce a modified version of the estimators proposed by Koyuncu (2013b) and Shahzad et al. (2019), as well as a new class of estimators. We derive expressions for the bias and mean squared error of these new estimators up to the first degree of approximation. Our results show that the suggested classes of estimators perform better than other existing methods, with the lowest mean squared error under optimal conditions. We also conduct an empirical investigation to support our findings.
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Affiliation(s)
- Housila P Singh
- School of Studies in Statistics, Vikram University, Ujjain, M.P., 456010, India
| | - Anurag Gupta
- Indian Agricultural Statistics Research Institute, ICAR, New Delhi, 110012, India.
| | - Rajesh Tailor
- School of Studies in Statistics, Vikram University, Ujjain, M.P., 456010, India
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A simulation study: Using dual ancillary variable to estimate population mean under stratified random sampling. PLoS One 2022; 17:e0275875. [PMID: 36441763 PMCID: PMC9704651 DOI: 10.1371/journal.pone.0275875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 09/23/2022] [Indexed: 11/29/2022] Open
Abstract
In this paper, we propose an improved ratio-in-regression type estimator for the finite population mean under stratified random sampling, by using the ancillary varaible as well as rank of the ancillary varaible. Expressions of the bias and mean square error of the estimators are derived up to the first order of approximation. The present work focused on proper use of the ancillary variable, and it was discussed how ancillary variable can improve the precision of the estimates. Two real data sets as well as simulation study are carried out to observe the performances of the estimators. We demonstrate theoretically and numerically that proposed estimator performs well as compared to all existing estimators.
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Hussain S, Akhtar S, El-Morshedy M. Modified estimators of finite population distribution function based on dual use of auxiliary information under stratified random sampling. Sci Prog 2022; 105:368504221128486. [PMID: 36168269 PMCID: PMC10450482 DOI: 10.1177/00368504221128486] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information due to its usefulness in estimation methods. The current study presents two new estimators for the distribution function of a finite population based on dual auxiliary variables. The new estimators can be used in situations where the researchers face some sort of complex data set. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator. Besides, an empirical study simulation study has also been conducted to analyse the performance of estimators. It is found that the new suggested estimators of the distribution function of a finite population are more accurate than some of the existing estimators.
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Affiliation(s)
- Sardar Hussain
- Department of Statistics, Quaid-i-azam University, Islamabad, Pakistan
| | - Sohail Akhtar
- Department of Mathematics and Statistics, The University of Haripur, Haripur, Pakistan
| | - Mahmoud El-Morshedy
- Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
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Yaqub M, Sohil F, Shabbir J, Sohail MU. Estimation of population distribution function in the presence of non-response using stratified random sampling. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2078492] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Mazhar Yaqub
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Fariha Sohil
- Department of Education, The Women University, Multan, Pakistan
| | - Javid Shabbir
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
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Hussain S, Ahmad S, Akhtar S, Javed A, Yasmeen U. Estimation of finite population distribution function with dual use of auxiliary information under non-response. PLoS One 2020; 15:e0243584. [PMID: 33332445 PMCID: PMC7746309 DOI: 10.1371/journal.pone.0243584] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2020] [Accepted: 11/23/2020] [Indexed: 11/18/2022] Open
Abstract
In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.
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Affiliation(s)
- Sardar Hussain
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Sohaib Ahmad
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Sohail Akhtar
- Department of Statistics, Government College University, Lahore, Pakistan
| | - Amara Javed
- Department of Statistics, Government College University, Lahore, Pakistan
- School of Statistics, Minhaj University, Lahore, Pakistan
| | - Uzma Yasmeen
- Institute of Molecular Biology and Biotechnology, The University of Lahore, Lahore, Pakistan
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