} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathop {\min }\limits_{{k_{3} ,k_{4} }} MSE\left( {T_{P2} } \right) \approx {\upmu }_{y}^{2} \left( {1 - \frac{{C_{2}^{2} \left( {A_{2} \, + B_{2} \, - 2\,\,E_{2} } \right)}}{{\Delta_{2} }}} \right)$$\end{document} The proposed estimators are highly significant than their counterparts, which will be assessed numerically in the coming sections with different real as well as synthetic data sets.
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Log-ratio type estimation for the finite population mean under simple random sampling without replacement with theory, simulation and application.
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