Abstract
Until now, various types of estimators have been used for estimating the population variance in simple random sampling studies, including ratio, product, regression and exponential-type estimators. In this article, we propose a family of -type estimators for the first time in the simple random sampling and show that they are more efficient than the other types of estimators under certain conditions obtained theoretically. Numerical illustrations and a simulation study support our findings in theory. In addition, it has been shown how to determine the optimal points in order to reach the minimum MSE values with the properties of the ln-type estimators in the different data sets.
Highlights
Different types of estimators have been proposed in the literature for estimating the population variance in simple random sampling, including ratio-type (Singh and Solanki 2013, Yadav et al 2015, Solanki et al 2015 and Kadilar and Cekim 2017), regression-type (Diana and Tommasi 2004, Kadilar and Cingi 2007 and Asghar et al 2017) and exponential-type (Yadav et al 2015, Yadav and Kadilar 2013) estimators
If the relationship is a straight line passing through the neighborhood of the origin, ratio and product estimators are equal to regression estimators
We propose the family of ln -type estimators for the population variance as tln Constant values j
Summary
Different types of estimators have been proposed in the literature for estimating the population variance in simple random sampling, including ratio-type (Singh and Solanki 2013, Yadav et al 2015, Solanki et al 2015 and Kadilar and Cekim 2017), regression-type (Diana and Tommasi 2004, Kadilar and Cingi 2007 and Asghar et al 2017) and exponential-type (Yadav et al 2015, Yadav and Kadilar 2013) estimators. Apart from these types of estimators, ln type estimators have used by Cekim and Kadilar (2020) in stratified random sampling methods and Hassan et al.
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