NONE 20260716100252389 wseas/wseas content-registration-form@crossref.org content-registration-form International Journal of Applied Mathematics Computational Science and Systems Engineering 2766-9823 Mojeed Abiodun Yunusa Department of Statistics, Usmanu Danfodiyo University, Sokoto, NIGERIA Awwal Adejumobi Department of Mathematics, Abdullahi Fodio University of Science and Technology, Aliero, NIGERIA Ahmed Audu Department of Statistics, Usmanu Danfodiyo University, Sokoto, NIGERIA Estimating variance is a common practice among statisticians particularly, survey statisticians. The estimate of variance gives information about the spread within the dataset, and allows the statisticians make vital decision about the event at hand at that moment. Existing variance estimators are function of unknown constants whose applicability is not possible in real life situation. In this paper, we intend to modify some existing variance estimators using coefficient of variation and kurtosis of auxiliary variable as auxiliary information that are free of unknown constants, and are applicable in real life situation. Optimization approach (Lagrange function) was used to obtain the calibration weights of newly proposed estimators and therefore the proposed calibration variance estimators were obtained. A simulation study was used to prove the better efficiency (minimum mean square error) of these proposed estimators. 07 16 2026 07 16 2026 126 12 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/232026.2026.8.12 https://wseas.com/journals/amcse/2026/a24amcse-012(2026).pdf Isaki, C. T. (1983). Variance estimation using auxiliary information. Journal of the American Statistical Association. 78(381), 117-123. Prasad, B. and Singh, H. P. (1992). Unbiased estimators of finite population variance using auxiliary information in sample surveys. 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