Construction of improved comprehensive classes of estimators for population distribution function

Area of Science:

• Statistics
• Survey Methodology

Background:

• Accurate estimation of finite population distribution functions (DFs) is crucial for data analysis.
• Existing methods may lack efficiency when auxiliary information is available.

Purpose of the Study:

• To develop and evaluate improved estimators for finite population DFs.
• To leverage auxiliary information like population mean and rank for better estimation.

Main Methods:

• Development of two novel DF estimators.
• Derivation of bias and mean squared error (MSE) for proposed and existing estimators.
• Validation using six real-world datasets and simulation analysis.

Main Results:

• The proposed estimators show improved performance compared to existing methods.
• Bias and MSE analyses confirm the efficiency of the new estimators.
• Numerical and simulation studies indicate the superiority of the suggested estimators.

Conclusions:

• The developed estimators offer a more accurate and efficient approach to finite population DF estimation.
• The findings are robust across diverse datasets and simulation scenarios.
• This research provides valuable tools for statisticians and data analysts working with finite populations.