An improved exponential ratio estimator for post-stratified sampling designs

Abstract

This study proposes a new ratio-type exponential estimator for estimating the finite population mean under post-stratification. A simple random sample is first selected and later divided into post-strata using an auxiliary variable to improve the precision of estimation. The proposed estimator incorporates auxiliary information obtained through post-stratification to reduce the mean squared error (MSE) compared with the usual unbiased estimator and some existing ratio-type estimators. Expressions for the bias and MSE of the estimator are derived to the first order of approximation, and the conditions under which the estimator performs more efficiently are established. To examine its practical usefulness, a real population dataset was employed and analysed. The performance of the proposed estimator was assessed using percentage relative efficiency (PRE) measures and compared with those of existing estimators available in the literature. The empirical results indicate that the proposed estimator produces smaller MSE values and higher efficiency values than the competing estimators. The findings therefore show that the estimator provides a more reliable and efficient approach for estimating the population mean, particularly in surveys involving stratified population data and the availability of relevant auxiliary information.