Quartile Double Rankled Set Sampling for Estimating the Population Mean

Abstract

Quartile Double Ranked Set Sampling (QDRSS) is investigated for estimating the population mean. The QDRSS estimators are compared to the simple random sampling (SRS), ranked set sampling (RSS) and quartile ranked set sampling (QRSS) estimators. It is shown that, the QDRSS estimators are unbiased for the population mean when the underlying distribution is symmetric, and have small biases when the underlying distribution is asymmetric. It turns out that the QDRSS is superior to the SRS, RSS and QRSS based on the same number of measured units. A real data set of "trees' olive yields" is used to illustrate the method. X 1(1:m) , X 2(2:m) , . . . , X m(m:m)(1)Assume that the variable of interest X has a density function f X and a distribution function F X with mean µ, and variance σ 2 . Let f (i:m) denote the density function of the ith, i = 1, . . . , m, order statistic denoted X (i:m) of a random sample of size m. Then, f (i:m) is given by:The mean and the variance of X (i:m) are given by:Brought to you by |

New ranked set sampling for estimating the population mean and variance

“…For m = 5, we have to select 25 units from the population and then measure only 5 units of them to be a neoteric ranked set sample, which are Y [3] , Y [8] , Y [13] , Y [18] , Y [23] . Therefore, the NRSS mean estimator is…”

“…Al-Saleh and Al-Omari [5], Al-Omari and Al-Saleh [3] and Al-Omari [1], [2] proposed some mean estimators in other variations of the RSS. Stokes [20] suggested an estimator of the population variance based on RSS and showed that it is asymptotically (n → ∞ or k → ∞) unbiased of the population variance and has greater efficiency than the sample variance using SRS regardless of the issue of ranking.…”