Hybrid Exponential Type Estimators of Finite Population Mean in Double Sampling

In this study, two-auxiliary exponential type estimators of finite population mean in Two-phase are proposed. The proposed estimators are extension of (1) estimator finite population mean in SRS to Two-phase sampling. The study investigated efficiency of the proposed estimators by utilizing the ratio of bias to standard error (RBSE) as a proxy to examine confidence limits for estimates. The expressions for the bias and Mean Square Error (MSE) of the estimators were derived. A comprehensive simulation study was carried out to show the efficacy of the estimators as compared to conventional estimators using Coefficient of Variation as a performance measure. Furthermore, a small sample from real data set was utilized to validate the performance of proposed estimators under two varying correlation coefficients amongst variables in the parameter space. The results of both the simulation study and real life studies have shown that the proposed estimators were not only asymptotic, more efficient but produces estimates that are more precise than most of the existing estimators considered in this study.