Estimation and Inference of Two Population Means within the Context of a Post-stratified Sampling Framework

This paper focuses on the estimation and inference of two population means within the context of a post-stratified sampling framework. Post-stratification is a widely used technique in survey sampling that aims to correct for imbalances in sample representation across strata, thereby improving the efficiency and reliability of population parameter estimates. The intent of this study was to resolve the estimation of ratio of two population means in case of post-stratification. To achieve this goal, we develop a novel estimator termed the ratio-cum-product exponential estimator. This estimator is constructed by combining ratio and product estimation techniques within an exponential framework to capitalize on auxiliary information more effectively. The mathematical properties of the proposed estimator are thoroughly analyzed, with particular attention given to its bias and mean square error (MSE). These properties are derived analytically up to the first order of approximation, allowing for a theoretical comparison with existing estimators commonly used in post-stratified sampling settings. To further validate the theoretical results, an empirical illustration is provided using real or simulated data. This application demonstrates the practical utility and performance gains of the developed estimator relative to traditional methods. The results confirm that the ratio-cum-product exponential estimator offers improved efficiency and reduced estimation error under certain conditions, thereby making it a valuable addition to the toolkit of survey statisticians and applied researchers.