Improved Estimation from Ranked Set Sampling

Abstract

Ranked set sampling is used when the measurement or quantification of units of the variable under study is difficult but the ranking of units of sets of small sizes can be done easily by an inexpensive method. Dell and Clutter (1972) showed that the sample mean based on ranked set sample is more efficient than the sample mean based on simple random sample with replacement sampling procedure for estimation of the population mean. In this paper Dell and Clutter estimator has been improved further by using the ranking variable x as an auxiliary variable when µx, the population mean of x is unknown. An empirical investigation based on life data shows all proposed estimators are approximately unbiased and bring gain in efficiency of up to 50 percent.

Stratified Two-Phase Ranked Set Sampling

“…Yu and Lam (1997) proposed regression estimator when x and y follow a bivariate normal distribution and found on the basis of simulation studies that their proposed regression estimator performs better than the naive estimator, unless the correlation between x and y is low (|ρ|< 0.4). Kadilar et al, (2006) and Arnab and Olaomi (2015) proposed an improved estimator of mean y  , the population mean of the study variable y using the ranking variable as an auxiliary variable x when the population mean x  of x is unknown. Zamanzade and Al-Omari (2016) developed a new ranked set sampling for estimating the population mean and variance, called neoteric ranked set sampling (NRSS) under perfect and imperfect ranking conditions while Mahdizadeh and Zamanzade (2018) introduced stratified pair ranked set sampling (SPRSS) and utilized it in estimating the population mean, with some theoretical results.…”