Bayesian and Non-Bayesian Parametric Estimation of the Bivariate Generalized Burr Distribution using Ranked Set Sampling with Concomitant Variable

Abstract

Ranked set sampling (RSS) has proven to be an efficient alternative to simple random sampling, particularly in situations where exact measurements are costly or difficult to obtain. Although extensive work has been devoted to parametric estimation under RSS for univariate models, relatively limited attention has been given to bivariate models, despite their importance in modeling dependence between random variables. In this paper, the likelihood function under ranked set sampling for the Marshal-Olkin bivariate class of distributions is derived in general and applies it on the bivariate generalized Burr distribution. Maximum likelihood estimation is considered for the model's unknown parameters. Bayesian estimation is also considered in both simple random sampling and ranked set sampling; moreover, the Bayes estimators are obtained explicitly with respect to the square error loss function in both cases.