An effective and economic estimation of population mean in stratified random sampling using a linear cost function

Area of Science:

• Statistics
• Sampling Theory

Background:

• Estimating population mean is crucial in statistics.
• Existing estimators in stratified random sampling have limitations in precision.
• There's a need for more accurate methods to estimate population mean.

Purpose of the Study:

• To propose a novel ratio-product-cum-exponential-cum-logarithmic type estimator.
• To enhance the estimation of population mean in stratified random sampling using an auxiliary variable.
• To generalize existing ratio, exponential ratio, and logarithmic ratio estimators.

Main Methods:

• Developed a new generalized estimator incorporating ratio, exponential, and logarithmic techniques.
• Analyzed the bias and Mean Squared Error (MSE) of the proposed estimator.
• Utilized Cramer's rule to find the optimal value of the estimator.
• Employed a linear cost function for comparative analysis.

Main Results:

• The proposed estimator is a generalization of existing estimators.
• Theoretical analysis indicates the proposed estimator is more effective than others.
• The bias and MSE of the proposed estimator were determined and compared.
• Optimal value determined using Cramer's rule.

Conclusions:

• The proposed estimator demonstrates superior performance compared to existing methods.
• The estimator has practical applicability, verified by a numerical example.
• Recommends using the proposed estimator for applications requiring minimal MSE.