Journal of Data Science

The concept of ranked set sampling (RSS) is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this work, we consider a study variable 𝑌 correlated with auxiliary variable 𝑋 which is used to rank the sampling units. Further (𝑋, 𝑌) is assumed to have Morgenstern type bivariate generalized uniform distribution. We obtain an unbiased estimator of a scale parameter associated with the study variable 𝑌 based on different RSS schemes and censored RSS. Efficiency comparison study of these estimators is also performed and presented numerically.

Abstract: In this paper, we obtain several estimators of a scale parameter of Morgenstern type bivariate uniform distribution (MTBUD) based on the observations made on the units of the ranked set sampling regarding the study variable Y which is correlated with the auxiliary variable X, when (X, Y ) follows a MTBUD. Efficiency comparisons among these estimators are also made in this work. Finally, we illustrate the methods developed by using a real data set.