Design-based estimators of the distribution function in ranked set sampling with an application

Abstract

Empirical distribution functions (EDFs) based on ranked set sampling (RSS) and its modifications have been examined by many authors. In these studies, the proposed estimators have been investigated for infinite population settings. However, developing EDF estimators in finite population settings would be more valuable for areas such as environmental, ecological, agricultural, biological, medical, etc. This paper introduces new EDF estimators based on level-0, level-1 and level-2 sampling designs in RSS. Asymptotic properties of the new EDF estimators have been established. Numerical results have been obtained for the case when ranking is imperfect under different distribution functions. It has been observed that level-2 sampling design provides a more efficient EDF estimator than its counterparts of level-0, level-1 and simple random sampling. In real data application, we consider a pointwise estimate of distribution function and estimation of the median of sheep's weights at 7 months using RSS based on level-2 sampling design.

Keywords:

• Design-based estimators
• empirical distribution function
• finite population
• ranked set sampling
• sheep data

Acknowledgments

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 author(s).

Additional information

Funding

The first author is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) 2211/A National PhD scholarship program and the Higher Education Council of Turkey (YÖK) 100/2000 PhD scholarship program.