In this paper we present an empirical nonlinear estimation model to explore two improved estimators over conventional estimator sample variance for estimating the population variance of a normal distribution by utilizing two auxiliary random variables and coefficient of variation (CV). Here, the proposed methodological framework involves sample mean and chi-square variate as two auxiliary random variables to obtain improved estimates of study variable. First estimator comprises of a combination of sample mean and sample variance as nonlinear statistic whereas the second estimator comprises of a nonlinear convex combination of mean and variance of the random sample. Essence properties including optimal values of characterizing scalars, bias and minimum mean square errors (MMSE) of the proposed estimators are derived successfully and discussed sensibly. Relative efficiencies of the proposed estimators are examined theoretically and empirically as well for moderate and large sample sizes. Numerical illustrations are demonstrated to observe the variation trends of relative efficiencies of the proposed estimators for varying key factors. Corresponding tables and graphs are presented using Microsoft Excel. By way of highlighting dominating properties of so obtained improved estimators over the sample variance, major issues pertaining to their validity and admissibility are discussed reasonably. Based on theoretical and empirical results, some significant conclusions are drawn to emphasize their key features and usefulness for future study. Finally, we remark here that the novelty of our findings lies in the fact that the proposed estimators are not only improved estimators over the sample variance due to their higher relative efficiencies but also the first one is asymptotically unbiased estimator of the population variance whereas another estimator is asymptotically unbiased estimator of the sample variance. Some related research works carried out by previous noteworthy contributors are also discussed by way of presenting its concise summary to enhance the usefulness of present work for future scope.

Keywords: Normal population, sample variance, chi-squared distribution, sampling distribution, central limit theorem, asymptotic unbiased estimator, coefficient of variation.

Prof. (Dr.) Vishwa Nath Maurya is the first great educationist and Executive Vice Chancellor of globally accredited American International University; who has demonstrated historically unique records as the highest qualified Vice Chancellor and laureate of multiple national & global awards for his significant contribution, outstanding performance and achievements in multidimensional fields of academic, administrative, scientific research and educational leadership. Prof. Maurya served as Head Examiner of Central Evaluation on several times at Chhatrapati Sahuji Maharaj University Kanpur and Dr. APJ Abdul Kalam Technical University, Lucknow, India during 2000-06. He was awarded first time for the rank of Full Professor, Head of Department of Applied Sciences & Engineering and Controller of Examinations in July 2004 at Singhania University Rajasthan, India (Formerly known as Singhania Institute of Law, Management, Arts, Science and Technology) by its founder Chancellor Adv. D.C. Singhania (international lawyer) and the Registrar Dr. G.D. Tripathi.

Degree of Doctor of Science (D.Sc.) in Sciences, Engineering & Technology and Management, and Doctor of Literatures (D.Litt.) in Public Administration and Finance Management from prestigious American International Universities for his research papers and multiple post-doctoral theses published worldwide as soul and principal author in peer reviewed global journals of Algeria, Austria, France, Georgia, Germany, India, Italy, Malaysia,, New Zealand, Nigeria,, UK., USA. Apart from regular/earned academic post-doctorate degrees from American Universities, Prof. Maurya has been honoured multiple honoris causa D.Litt. and D.Sc. in Faculty of Sciences, Engineering and Management from well recognized African Asian and Canadian Universities. Very recently, Da Vinci University, USA’s Executive Vice-Chancellor Prof. (Dr.) Vishwa Nath Maurya has been honored for double post-Doctorate Honorary Causa Degrees of Doctor of Literature (D.Litt.) in Business Administration and Finance Management, and Doctor of Sciences (D.Sc.) in Mathematical, Statistical and Computational Sciences by the Chancellor and President of Lighthouse Leadership University, Recognized by Registrar General of Corporate Affairs Commission, Federal Republic of Nigeria.

reviewed journals, and over 250 articles on miscellaneous issues of community services have been published in memorious national and international newspapers. As an international distinguished mathematician, statistician, data analyst and management scientist Professor Dr. V.N. Maurya played key role of advisory member of International Scientific Committee of Mathematical and Computational Sciences, and research committees of International Conferences organized worldwide by the World Academy of Science, Engineering and Technology (WASET) Italy; Institute of Research Engineers and Doctors (IRED) USA and Institute of Electrical and Electronics Engineers (IEEE), the world's largest technical professional organization for the advancement of technology and Innovation Society, New Delhi, India.