Parameter estimation of Cambanis-type bivariate uniform distribution with Ranked Set Sampling.

Area of Science:

• Statistics
• Statistical Inference
• Sampling Theory

Background:

• Ranked Set Sampling (RSS) is effective when judgment ranking or auxiliary variables simplify unit assessment.
• Auxiliary variables correlated with study variables can enhance sampling efficiency.
• The Cambanis-type bivariate uniform (CTBU) distribution offers a specific model for bivariate data.

Purpose of the Study:

• To develop unbiased estimators for a scale parameter of a study variable using RSS.
• To evaluate the efficiency of these estimators under different RSS schemes.
• To assess the performance of estimators using numerical comparisons, simulations, and real-data application.

Main Methods:

• Utilizing an auxiliary variable correlated with the study variable for ranking units in RSS.
• Assuming the study variable follows a Cambanis-type bivariate uniform (CTBU) distribution.
• Deriving unbiased estimators for the scale parameter and comparing their efficiency numerically and via simulation.

Main Results:

• The proposed unbiased estimators demonstrate varying degrees of efficiency across different RSS schemes.
• Numerical and simulation studies confirm the efficiency trends of the estimators.
• The performance of the estimators is validated through application to real-life data.

Conclusions:

• Ranked Set Sampling, utilizing correlated auxiliary variables and the CTBU distribution, provides effective methods for scale parameter estimation.
• The study offers practical insights into the efficiency of different RSS schemes for statistical inference.
• The developed methods and simulations are applicable to both theoretical and applied statistical problems.