Empirical distribution function estimators based on sampling designs in a finite population using single auxiliary variable

ABSTRACT

In this paper, we study empirical distribution function (EDF) estimators based on ranked set sampling (RSS). Ranked set samples are constructed by using three different sampling designs which are level-0, level-1 and level-2. These designs are different in terms of their replacement policies. The sample is constructed by sampling with replacement in level-0 sampling design. In level-1 sampling design, the sample is constructed by sampling with replacement of the unmeasured units in each set. Also, we construct the sample without replacement on the entire set in level-2 sampling design. In simulation study, we compare EDF estimators when using sampling designs with EDF estimator when using simple random sampling (SRS) in finite populations having different distribution functions. The effects of both perfect and imperfect ranking on the estimators of the sampling designs are investigated. Relative efficiencies of the EDF estimators are obtained by using their integrated mean squared errors (IMSEs), numerically. For illustrative purposes, these EDF estimators based on sampling designs are applied to a real data set. By using both the simulation data and real data, we show that these EDF estimators have higher efficiencies against EDF based on SRS.

KEYWORDS:

• Empirical distribution function
• ranked set sampling
• sampling designs
• auxiliary variable
• integrated mean squared error
• relative efficiency

Acknowledgements

The authors thank the reviewers and the editor for helpful comments that have improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.