Concomitants of Order Statistics from a Bivariate Generalized Linear Exponential Distribution: Theory and Practice

Area of Science:

• Statistics
• Probability Theory

Background:

• Order statistics and their concomitants are crucial in statistical inference.
• The bivariate generalized linear exponential (BGLE) distribution offers a flexible model for bivariate data.

Purpose of the Study:

• To investigate the properties of concomitants of order statistics from the BGLE distribution.
• To derive the probability density functions (PDFs) and moments of these concomitants.
• To apply these findings to parameter estimation using ranked set sampling.

Main Methods:

• Derivation of the PDF for a single concomitant and the joint PDF for two concomitants.
• Calculation of single and product moments for the concomitants.
• Development of the best linear unbiased estimator (BLUE) for a scale parameter.

Main Results:

• Explicit formulas for the PDFs and moments of BGLE distribution concomitants were obtained.
• The study established methods for estimating scale parameters using ranked set sampling.
• The practical utility was demonstrated through application to a real dataset.

Conclusions:

• The research provides a theoretical framework for understanding BGLE distribution concomitants.
• The derived estimators offer efficient methods for scale parameter estimation.
• The findings have implications for statistical modeling and data analysis in various fields.