Improved estimation of population distribution function using twofold auxiliary information under simple random...

Area of Science:

• Statistics
• Statistical Inference
• Survey Sampling

Background:

• Accurate estimation of population distribution functions (DF) is crucial in statistical analysis.
• Existing methods may lack efficiency when incorporating auxiliary information.
• Simple random sampling is a fundamental technique, but enhancements are needed.

Purpose of the Study:

• To propose enhanced families of estimators for population DF estimation.
• To utilize twofold auxiliary information within simple random sampling.
• To improve the precision and efficiency of distribution function estimation.

Main Methods:

• Development of novel estimator families incorporating auxiliary variables.
• Empirical validation using four real-world datasets.
• Simulation studies to assess estimator performance and precision.

Main Results:

• The proposed estimators achieved minimum mean square error (MSE).
• Enhanced percentage relative efficiency (PRE) was observed compared to existing estimators.
• A specific recommended family consistently outperformed others across datasets.

Conclusions:

• The suggested estimator families offer significant improvements in estimating population distribution functions.
• The enhanced methods provide superior performance in terms of MSE and efficiency.
• The findings highlight the practical utility of the proposed estimators in statistical surveys.