An Improved Estimation of Population Mean Using Auxiliary Attribute in Stratified Sampling

Abstract

Stratification improves the efficiency when the variance between strata is much larger than the variances within strata. An exponential estimator for stratified random sampling was proposed. Data sets on the amount of Apple production taken at three different occasions in Turkey in 1999 were used to validate the proposed estimator. The data sets were stratified by regions of Turkey and from each region; we randomly selected the samples by using the Neyman allocation method. Expressions for MSE of the proposed estimators were derived, up to first order of approximation. The suggested estimator families' bias and MSE equations were computed, the MSE for the proposed estimators is unbiased and efficient. The results of the theoretical comparison and numerical analysis shows that the suggested estimator outperformed the existing estimator. Moreover, the derived exponential estimator performed better than existing estimators for estimating population mean in stratified random sampling with an auxiliary attribute.