A Generalized Approach for Estimation of a Finite Population Mean in Two-Phase Sampling
Ashish Tiwari
Department of Agricultural Statistics, Acharya Narendra Deva University of Agriculture and Technology, Ayodhya- 224229, India.
Manish Kumar *
Department of Agricultural Statistics, Acharya Narendra Deva University of Agriculture and Technology, Ayodhya- 224229, India.
Sarvesh Kumar Dubey
Department of Agricultural Statistics, Acharya Narendra Deva University of Agriculture and Technology, Ayodhya- 224229, India.
*Author to whom correspondence should be addressed.
Abstract
The present paper deals with the formulation of a generalized class of ratio-cum-product estimators for the estimation of a finite population mean in two-phase sampling. The mathematical expressions for the mean square errors (MSEs) of the preliminary and proposed estimators are derived. It has been established that the proposed class encompasses a wide range of estimators for specific choices of the scalars. The relative performance of the proposed class, as compared to the preliminary estimators, is evaluated using the MSE criterion. In addition, optimum sample sizes of the first-phase and second-phase samples are obtained using a specified cost function. The theoretical findings are empirically assessed by computing MSEs and percent relative efficiencies (PREs) of various estimators based on real population datasets. The findings of the study reveal that the proposed class of estimators are superior as compared to the preliminary estimators for the estimation of mean.
Keywords: Study variable, auxiliary variable, two-phase sampling, cost function analysis, mean square error, percent relative efficiency