An improved ratio-cum-exponential estimator for finite population mean with properties: Applications to radiation monitoring and economic management data

In simple random sampling without replacement (SRSWOR), auxiliary information is an important component for improving the precision of estimators of finite population means. Although a few estimators have been developed to combine dual auxiliary information using a ratio-cum-exponential structure, most estimators rely on a single auxiliary variable, either through ratio, product, or regression structures. This study presents a new ratio/cu-exponential estimator for estimation of the finite population mean by combining two auxiliary variables in an optimized exponential structure. We determine the bias and mean squared error (MSE) of the proposed estimator using a first-order approximation method, and we determine the optimal values of the characterizing constants analytically. We formulate conditions for theoretical efficiency to compare the proposed estimator with conventional estimators such as the sample mean, ratio, product, regression, exponential, and existing dual auxiliary estimators. We also use a real dataset from a radiation monitoring and economic management application to evaluate the proposed estimator’s performance in terms of MSE and PRE. The results show that the proposed estimator has uniformly lower MSE and PRE than the other estimators across various correlation structures and population characteristics. The proposed ratio-cum-exponential estimator has been verified to be a powerful and efficient method for estimating finite population means in various scientific, physical, and socio-economic settings.