{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T10:35:03Z","timestamp":1770546903278,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T00:00:00Z","timestamp":1721952000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["KFU241416"],"award-info":[{"award-number":["KFU241416"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This article suggests an improved class of efficient estimators that use various transformations to estimate the finite population variance of the study variable. These estimators are particularly helpful in situations where we know about the minimum and maximum values of the auxiliary variable, and the ranks of the auxiliary variable are associated with the study variable. Consequently, these rankings can be applied as an effective tool to improve the accuracy of the estimator. A first-order approximation is used to investigate the properties of the proposed class of estimators, such as bias and mean squared error (MSE) under simple random sampling. A simulation study carried out in order to measure the performance and verify the theoretical results. The suggested class of estimators has a greater percent relative efficiency (PRE) than the other existing estimators in all of the simulated situations, according to the results. Three symmetric and asymmetric datasets are examined in the application section in order to show the superior performance of the proposed class of estimators over the existing estimators.<\/jats:p>","DOI":"10.3390\/sym16080957","type":"journal-article","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T14:39:08Z","timestamp":1722004748000},"page":"957","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Variance Estimation under Some Transformation for Both Symmetric and Asymmetric Data"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5702-9806","authenticated-orcid":false,"given":"Umer","family":"Daraz","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha 410017, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-4064-5598","authenticated-orcid":false,"given":"Mohammed Ahmed","family":"Alomair","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7772-0386","authenticated-orcid":false,"given":"Olayan","family":"Albalawi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,26]]},"reference":[{"key":"ref_1","first-page":"93","article-title":"A note on improving the ratio method of estimation through linear transformation using certain known population parameters","volume":"57","author":"Mohanty","year":"1995","journal-title":"Sankhy\u0101 Indian J. 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