Abstract
In this paper, we have proposed an estimator of finite population mean in stratified random sampling. The expressions for the bias and mean square error of the proposed estimator are obtained up to the first order of approximation. It is found that the proposed estimator is more efficient than the traditional mean, ratio, exponential, regression, Shabbir and Gupta (in Commun Stat Theory Method 40:199–212, 2011) and Khan et al. (in Pak J Stat 31:353–362, 2015) estimators. We have utilized four natural and four artificial data sets under stratified random sampling scheme for assessing the performance of all the estimators considered here.
Highlights
Stratification is a designing tool that is used in modern surveys for improving the precision of estimates
The fundamental goal of this paper is to propose an improved estimator of the finite population mean utilizing data on an auxiliary variable in stratified random sampling
The rest of the paper is organized as follows: ‘‘Some existing estimators’’ section consists in the estimators which we reviewed from the literature, and some useful preliminaries results for obtaining the properties of proposed and existing estimators are available here. ‘‘Proposed estimator’’ section introduces an improved estimator using stratified random sampling scheme. ‘‘Numerical illustration’’ section is devoted to the efficiency comparison
Summary
Stratification is a designing tool that is used in modern surveys for improving the precision of estimates. There are numerous authors who have suggested different estimators by utilizing some known population parameters of an auxiliary variable. Singh and Kakran [9] proposed another proportion estimator by utilizing known coefficient of kurtosis of an auxiliary variable. The fundamental goal of this paper is to propose an improved estimator of the finite population mean utilizing data on an auxiliary variable in stratified random sampling. The expressions for the bias and mean square error (MSE) of the proposed estimator are inferred up to the first order of approximation. Let X be an auxiliary and Y be the study variable taking values yhi and xhi in the unit ði 1⁄4. The bias and MSE of classical ratio estimator given in (1) up to the first order of approximation are given below: Biasðy^RstÞ 1⁄4Y1⁄2V0:2 À V1:1 MSEðy^RstÞ 1⁄4Y21⁄2V2:0 þ V0:2 À 2V1:1: ð2Þ. The bias and MSE of y^BTst up to the first order of approximation are given below:
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