A Generalized Class of Log-Type Estimators of Finite Population Mean Based on Correlation Coefficient

Abstract

In sampling theory, it is a popular trend to use auxiliary information to obtain more efficient estimators for the population parameters to increase the precision of the estimator. Estimators obtained using auxiliary information are supposed to be more efficient than the estimators obtained without using auxiliary information. The ratio, regression, product and difference methods take advantage of the auxiliary information at the estimation stage. Therefore, this study considered a generalized class of log-type estimators of finite population mean based on correlation coefficient as the proposed estimator for estimating the population mean of the study variable. It has been shown that the generalized class of log-type estimators has lesser mean square errors (MSEs) under the optimum values of the characterizing scalar as compared to some of the commonly used related estimators available in the literature. Further, an extension of the proposed generalized class of log-type estimators using multiple auxiliary variables such as coefficient of variation, coefficient of kurtosis , and correlation coefficient. have also base initiated in this dissertation. The expressions for the properties of the proposed family of estimators, that is; Bias and Mean Square Error (MSE), were derived to the first degree of approximation. We also obtained the optimum Mean Square Error (MSE_opt.), and theoretical comparisons were made with the related existing estimators in literature. Following theoretical comparisons, it was demonstrated that the proposed family of estimators was more efficient than various related existing estimators compared with, under the obtained conditions.