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

Abstract

The concept of ranked set sampling (RSS) is applicable whenever ranking on a set of sampling units can be done easily using a judgment method or based on an auxiliary variable. In this paper, we consider a study variable $Y$ correlated with the auxiliary variable $X$ and use it to rank the sampling units. Further $(X,Y)$ is assumed to have Cambanis-type bivariate uniform (CTBU) distribution. We obtain an unbiased estimator of a scale parameter associated with the study variable $Y$ based on different RSS schemes. We perform the efficiency comparison of the proposed estimators numerically. We present the trends in the efficiency performance of estimators under various RSS schemes with respect to parameters through line and surface plots. Further, we develop a Matlab function to simulate data from CTBU distribution and present the performance of proposed estimators through a simulation study. The results developed are implemented to real-life data also.

KEYWORDS:

• Ranked set sampling
• concomitants of order statistics
• Cambanis-type bivariate uniform distribution
• best linear unbiased estimator

SUBJECT CLASSIFICATIONS:

• 62D05
• 62F07
• 62G30

Acknowledgements

The authors are highly grateful to the referees for their constructive and valuable comments, which led to a considerable improvement in the present version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.