Improved modified estimator for estimation of median using auxiliary information under simple random sampling.

Area of Science:

• Statistics
• Statistical Inference

Background:

• Accurate estimation of population parameters is crucial in statistical analysis.
• Auxiliary information can enhance the precision of estimators.
• Simple random sampling is a fundamental sampling technique.

Purpose of the Study:

• To propose an improved estimator for the population median.
• To utilize auxiliary information within a simple random sampling framework.
• To evaluate the efficiency of the proposed estimator against existing ones.

Main Methods:

• Derivation of bias and mean square error (MSE) expressions up to first-order approximation.
• Determination of the maximum likelihood estimator (MLE) for optimal scalar values.
• Comparative analysis using MSE and percentage relative efficiency (PRE) metrics.

Main Results:

• The proposed estimator achieves lower MSE compared to existing estimators.
• The new estimator demonstrates higher PRE, indicating improved efficiency.
• Both theoretical and empirical studies confirm the estimator's superior performance.

Conclusions:

• The developed estimator offers a statistically significant improvement for population median estimation.
• The use of auxiliary information effectively enhances estimation accuracy.
• The findings provide a more efficient tool for statistical inference in similar studies.