Monte Carlo Methods Appl. 18 (2012), 109 – 118 DOI 10.1515 / mcma-2012-0002 © de Gruyter 2012 On the population median estimation using robust extreme ranked set sampling Amer Ibrahim Al-Omari and Amjad D. Al-Nasser Abstract. In this paper, the robust extreme ranked set sampling (RERSS) scheme is con- sidered for estimating the population median. The RERSS is compared with the simple random sampling (SRS), ranked set sampling (RSS) and extreme ranked set sampling (ERSS) schemes. A Monte Carlo simulation study is used to study the performance of the median estimator. It is found that RERSS estimators are unbiased of the population median when the underlying distribution is symmetric. Also, in terms of the efficiency cri- terion; the median estimator based on RERSS is more efficient than the median estimators based on SRS, ERSS, and RSS for symmetric and asymmetric distributions considered in this study. For asymmetric distributions, the RERSS estimators have a smaller bias. Keywords. Ranked set sampling, robust extreme ranked set sampling, efficiency, Monte Carlo simulation. 2010 Mathematics Subject Classification. 94A20, 78M31, 62G35. 1 Introduction The RSS was first suggested by McIntyre (1952) for estimating the mean pasture and forage yields. Later, Takahasi and Wakimoto (1968) studied the mathematical properties of the method. After then, many authors suggested different select- ing mechanisms of the sampling units based on the novel idea of RSS; Samawi et al. (1996) suggested extreme ranked set samples (ERSS) for estimating a pop- ulation mean. Muttlak (1997) suggested using median ranked set sampling in estimating the population mean. Jemain and Al-Omari (2006) suggested double quartile ranked set samples for estimating the population mean. Al-Nasser (2007) suggested L ranked set sampling as a generalization robust sampling method. Al- Nasser and Bani-Mustafa (2009) suggested a robust extreme ranked set sampling for estimating the population mean and showed that the estimator is an unbiased and more efficient than SRS when the underlying distribution is symmetric. Brought to you by | Purdue University Libraries Authenticated Download Date | 5/29/15 7:36 PM