Estimating the population mean using extreme ranked set sampling

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSS_s) to estimate the population mean ERSS_s is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSS_s gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.