Modified BLUEs and BLIEs of the location and scale parameters and the population mean using ranked set sampling

Abstract

Ranked set sampling (RSS) is a sampling procedure that can be used to improve the cost efficiency of selecting sample units of an experiment or a study. In this paper, RSS is considered for estimating the location and scale parameters a and b>0, as well as the population mean from the family F((x−a)/b). Modified best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) are considered. Numerical computations with different location-scale distributions and different sample sizes are conducted to assess the efficiency of the suggested estimators. It is found that the modified BLIEs are uniformly higher than that of BLUEs for all distributions considered in this study. The modified BLUE and BLIE are more efficient when the underlying distribution is symmetric.

Keywords:

• ranked set sampling
• simple random sampling
• location parameter
• scale parameter
• best linear unbiased estimator
• best linear invariant estimator

Acknowledgements

The authors would like to thank the referees for their thorough review of the paper. The first and second authors are grateful to the University of Jordan for supporting this research work.

Notes

^†This work is a part of M. Sc. thesis of Maisa R. Shadid, under the supervision of Professor M. Raqab, Department of Mathematics, University of Jordan.