{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T21:58:08Z","timestamp":1790891888988,"version":"4.1.0"},"reference-count":30,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T00:00:00Z","timestamp":1716163200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University, Riyadh, Saudi Arabia","doi-asserted-by":"publisher","award":["RSPD2024R749"],"award-info":[{"award-number":["RSPD2024R749"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The traditional stratification weight is widely used in survey sampling for estimation under stratified random sampling (StRS). A neutrosophic calibration approach is proposed under neutrosophic statistics for the first time with the aim of improving conventional stratification weight. This addresses the challenge of estimating the empirical cumulative distribution function (CDF) of a finite population using the neutrosophic technique. The neutrosophic technique extends traditional statistics, dealing with indeterminate, vague, and uncertain values. Thus, using additional information, we are able to obtain an effective estimate of the neutrosophic CDF. The suggested estimator yields an interval range in which the population empirical CDF is likely to exist rather than a single numerical value. The proposed family of neutrosophic estimators will be defined under suitable calibration constraints. A simulation study is also computed in order to assess the effectiveness of the suggested and adapted neutrosophic estimators using real-life symmetric and asymmetric datasets.<\/jats:p>","DOI":"10.3390\/sym16050633","type":"journal-article","created":{"date-parts":[[2024,5,20]],"date-time":"2024-05-20T11:06:41Z","timestamp":1716203201000},"page":"633","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Calibrated Empirical Neutrosophic Cumulative Distribution Function Estimation for Both Symmetric and Asymmetric Data"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1720-9698","authenticated-orcid":false,"given":"Hareem","family":"Abbasi","sequence":"first","affiliation":[{"name":"Department of Statistics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0178-5298","authenticated-orcid":false,"given":"Usman","family":"Shahzad","sequence":"additional","affiliation":[{"name":"Department of Statistics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan"},{"name":"Department of Business Administration, Hunan University, Changsha 410082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Hanif","sequence":"additional","affiliation":[{"name":"Department of Statistics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nasir","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Statistics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mubeen","family":"Mukhtar","sequence":"additional","affiliation":[{"name":"Department of Statistics, PMAS-Arid Agriculture University, Rawalpindi 46300, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"114214","DOI":"10.1016\/j.cam.2022.114214","article-title":"Predictive estimation approach using difference and ratio type estimators in ranked set sampling","volume":"410","author":"Bhushan","year":"2022","journal-title":"J. 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