Abstract
In this paper, percentile double ranked set sampling (PDRSS) method is suggested for estimating the population mean. The PDRSS method is compared with the simple random sampling (SRS), ranked set sampling (RSS), median ranked set sampling (MRSS) and the extreme ranked set sampling (ERSS) methods. When the underlying distribution is symmetric, it turns out that PDRSS produce unbiased estimators of the population mean and it is more efficient than SRS, RSS, MRSS and ERSS based on the same sample size. For asymmetric distribution considered in this study, it is shown that PDRSS has a small bias and it is more efficient than RSS, MRSS and ERSS for most cases considered in this study.
Highlights
Ranked set sampling (RSS) is a cost effective sampling procedure when compared to the commonly used simple random sampling (SRS) in the situations where visual ranking of units of m units, the second smallest ranked unit is measured
The procedure of ranked set sampling is applied on these sets to obtain m ranked set sampling each of size m, again apply the ranked set sampling procedure on the m ranked set sampling sets to obtain a double ranked set sampling method (DRSS) of size m
Estimation of the population mean: Let X1, X 2,..., X m be a random sample with probability density function f (x) with mean μ and variance σ2
Summary
Ranked set sampling (RSS) is a cost effective sampling procedure when compared to the commonly used SRS in the situations where visual ranking of units of m units, the second smallest ranked unit is measured. The process is continued until from the mth set of m units the largest ranked unit is measured. Repeat the process n times if needed to obtain a set of size mn from initial m2n units. McIntyre [4] proposed the sample mean based on RSS as an estimator of the population mean. He found that the estimator based on RSS is more efficient than SRS. Many modifications on RSS have been done since McIntyre [4]. Samawi and Muttlak [6] suggested RSS
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