{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T07:44:08Z","timestamp":1777362248493,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T00:00:00Z","timestamp":1736208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSPD2025R749"],"award-info":[{"award-number":["RSPD2025R749"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce a new, improved family of estimators aimed at improving the accuracy of finite population variance estimation. The proposed class of estimators is enhanced in terms of overall estimating performance and robustness by using the maximum and minimum values as supplementary information to improve precision and reliability. The bias and mean square error are theoretically obtained to the first order of approximation. We carried out a simulation study to evaluate the performance of the proposed estimators and validate the theoretical results. The findings show that the proposed estimators have higher percent relative efficiencies than the existing estimators across all of the simulated scenarios. Additionally, three independent symmetric and asymmetric datasets are analyzed to further confirm the better efficiency of proposed estimators compared with traditional estimators.<\/jats:p>","DOI":"10.3390\/sym17010084","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T10:45:55Z","timestamp":1736246755000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Finite Population Variance Estimation Using Monte Carlo Simulation and Real Life Application"],"prefix":"10.3390","volume":"17","author":[{"given":"Umer","family":"Daraz","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410017, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8608-1977","authenticated-orcid":false,"given":"Jinbiao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410017, China"}]},{"given":"Della","family":"Agustiana","sequence":"additional","affiliation":[{"name":"School of Metallurgy and Environment, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6810-6640","authenticated-orcid":false,"given":"Walid","family":"Emam","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1080\/01621459.1938.10503378","article-title":"Contribution to the theory of sampling human population","volume":"33","author":"Neyman","year":"1938","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1080\/01621459.1962.10500551","article-title":"Some ratio-type estimators in two-phase sampling","volume":"57","author":"Sukhatme","year":"1962","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_3","unstructured":"Cochran, W.B. (1963). Sampling Techniques, John Wiley and Sons."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/01621459.1983.10477939","article-title":"Variance estimation using auxiliary information","volume":"78","author":"Isaki","year":"1983","journal-title":"J. Am. Stat. 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