RATIO AND PRODUCT TYPE EXPONENTIAL ESTIMATORS OF POPULATION VARIANCE UNDER TRANSFORMED SAMPLE INFORMATION OF STUDY AND SUPPLEMENTARY VARIABLES
AUDU AHMED *
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.
RAN VIJAY KUMAR SINGH
Department of Mathematics, Kebbi State University of Science and Technology, Aliero, Nigeria.
ADEDAYO AMOS ADEWARA
Department of Statistics, University of Ilorin, Kwara State, Nigeria.
*Author to whom correspondence should be addressed.
In this paper, we have suggested a class of modified ratio and product exponential estimators for finite population variance. The proposed class of exponential estimators was obtained by transforming both the sample variances and means of study and auxiliary variables of Singh et al.  and Asgha et al.  estimators. The mean square errors (MSEs) of the proposed estimators have been obtained and the conditions for their efficiency over some existing variance estimators have been established. The efficiency of proposed estimators based on optimal values of the constants, exhibit significant improvement over the estimators considered in the study. The numerical illustration was also conducted to corroborate the theoretical results. The result of the empirical study does not only show high efficiency of the proposed class of estimators over existing estimators but also save cost because their efficiency is high for small samples.
Keywords: Efficiency, mean square error, exponential estimator, finite population, variance