Abstract
This paper introduces ratio estimators of the population mean using the coefficient of variation of study variable and auxiliary variables together with the coefficient of correlation between the study and auxiliary variables under simple random sampling and stratified random sampling. These ratio estimators are almost unbiased. The mean square errors of the estimators and their estimators are given. Sample size estimation in both sampling designs are presented. An optimal sample size allocation in stratified random sampling is also suggested. Based on theoretical study, it can be shown that these ratio estimators have smaller MSE than the unbiased estimators. Moreover, the empirical study indicates that these ratio estimators have smallest MSE compared to the existing ones.
Highlights
Consider a population of N units with observations x i, y i for i 1, 2, N where y i is a value of study variable and x i is a value of auxiliary variable
The optimum ratio estimator and its variance estimate depend on the coefficient of variation, the coefficient of correlation and the mean of the auxiliary variable in the whole population
The optimum separate ratio estimator and its variance estimate are in terms of the coefficients of variation, the coefficient of correlation and the means of the auxiliary variable in all strata
Summary
Consider a population of N units with observations x i , y i for i 1, 2, , N where y i is a value of study variable and x i is a value of auxiliary variable. Under simple random sampling without replacement, an unbiased estimator of the population mean. X x where X and x are the population and sample means of the auxiliary variable, respectively. The efficiency of the ratio estimator depends on the coefficient of variation of auxiliary variable C x and coefficient of variation of study variable C y . Murthy (1964) has suggested that if. The ratio estimator performs better than the unbiased estimator where is the correlation coefficient between x and y. The approximate bias and mean square error (MSE) of the ratio estimator are as follows:
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