Some Novel Logarithmic Type Estimators for the Finite Population Mean using Auxiliary Information

Abstract

The incorporation of auxiliary information has become a vital component in the process of statistical estimation, as it substantially enhances the accuracy of estimators for population parameters such as the mean and variance of the study variable. Over the years, several methodologies including the ratio, product, and regression estimators have gained recognition for their effectiveness in this regard. Building on these classical approaches, the present paper introduces some novel and efficient logarithmic ratio-type estimators for estimating the finite population mean under simple random sampling. To analyze the performance of the proposed estimator, mathematical expressions for its bias and mean squared error (MSE) are derived, up to the first-order approximation. Furthermore, the specific conditions under which the proposed estimator demonstrates greater efficiency than the conventional estimators are clearly established. To support the theoretical results, an empirical investigation using two datasets is carried out, together with a simulation study. The findings of this analysis strongly indicate that the proposed logarithmic ratio-type estimator consistently outperforms the competing estimators considered in the study, thereby validating its practical utility.