A General Class of Difference-Cum-Ratio-Type Exponential Estimators for Finite Population Mean by Using Dual Auxiliary Information in Stratified Random Sampling

When a sufficiently strong correlation exists between the study variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>Y</mml:mi> </mml:math> and the auxiliary variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>X</mml:mi> </mml:math> , the ranks of the auxiliary variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:mrow> </mml:math> are also correlated with the values of the study variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>Y</mml:mi> </mml:math> . As a result, these ranks can enhance the precision of the estimators. In this article, we propose a general class of difference-cum-ratio-type exponential estimators for the finite population mean under the stratified random sampling scheme, utilizing both the auxiliary variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>X</mml:mi> </mml:math> and its rank <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:mrow> </mml:math> . Up to first-order of approximation, we derive the mathematical expressions for the bias and mean squared error (MSE) of the proposed estimator, as well as for other existing estimators. We apply the proposed method to two real data sets, and a simulation study is carried out using an artificially generated bivariate population to observe the performance of the estimators. The results indicate that the proposed estimator consistently yields a lower MSE and higher relative efficiency compared to other existing estimators. The numerical evidence demonstrates that the proposed estimator outperforms all other existing alternatives in various scenarios. We conclude that the general class of estimators presented in this study exhibits superior performance compared to all other existing estimators. AMS Subject Classification: MSC2020, 62D05