Abstract
One of the aims in survey sampling is to search for the estimators with highest efficiency. In the present paper, three improved estimators of population mean have been proposed using some non-traditional measures of dispersion of auxiliary variable such as Gini’s mean difference, Downton’s method and probability weighted moments early given by Abid [1] with a special population parameter of auxiliary variable. The large sample properties that are biased and mean squared errors of the proposed estimators have been derived up to the first order of approximation. A theoretical comparison of the proposed estimators has been made with the other existing estimators of population mean using auxiliary information. The conditions under which the proposed estimators perform better than the other existing estimators of population mean have been given. A numerical study is also carried out to see the performances of the proposed and existing estimators of population mean and verify the conditions under which proposed estimators are better than other estimators. It has been shown that the proposed estimators perform better than the existing estimators as they are having lesser mean squared error.
Highlights
Sampling is done when the population is very large and we have to get the result very soon
Three improved estimators of population mean have been proposed using some non-traditional measures of dispersion of auxiliary variable such as Gini’s mean difference, Downton’s method and probability weighted moments early given by Abid [1] with a special population parameter of auxiliary variable
When the auxiliary variable is positively correlated with the main variable under study, ratio type estimators are used for improved estimation of population parameters
Summary
Sampling is done when the population is very large and we have to get the result very soon. As it has been mentioned that the most suitable estimator for the estimation of population parameter is the corresponding statistics so to estimate population mean the most suitable estimator is the sample mean. K. Yadav reasonably large variance and our aim is to search for the estimator with minimum variance or may be biased but with minimum mean squared error. Yadav reasonably large variance and our aim is to search for the estimator with minimum variance or may be biased but with minimum mean squared error This purpose is solved through the use of auxiliary information. When the auxiliary variable is positively correlated with the main variable under study, ratio type estimators are used for improved estimation of population parameters. We have confined our study to positively correlated populations only and proposed three ratio type estimators for improved estimation of population mean with higher efficiencies
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