Product in Product Type Estimator with Exponential and Log Function to Estimate Population Mean Using DSS

To estimate the population, mean in two-phase stratified sampling, this paper aims to construct a new product in the product type estimator using exponential and log functions. When using two samples for stratification, this study attempts to solve the equation for bias and mean squared error (MSE) up to the first degree of approximation (fda). The modified estimator is more effective than \(\bar{y}_{ds}\) (the usual unbiased estimator, \(\hat{Y}^{ds}_{PP}\) (Ige & Tripathi ratio estimator) and \(\hat{Y}_{PPe}\) (ratio type exponential estimator) given by Tailor et al. theoretically and numerically. Finding out how the proposed estimators stack up against the state-of-the-art is the main motivation for this research. Extensive evaluation of the estimator's performance in a simulated environment. The suggested estimators perform better than other estimators, according to both theoretical and practical studies.