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Weighted Ranked Set Sampling for Skew Distributions
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Version 1
: Received: 29 May 2024 / Approved: 30 May 2024 / Online: 30 May 2024 (13:27:22 CEST)
A peer-reviewed article of this Preprint also exists.
Bhoj, D.S.; Chandra, G. Weighted Ranked Set Sampling for Skewed Distributions. Mathematics 2024, 12, 2023. Bhoj, D.S.; Chandra, G. Weighted Ranked Set Sampling for Skewed Distributions. Mathematics 2024, 12, 2023.
Abstract
Ranked Set Sampling (RSS) is a useful technique for improving the estimator of population mean when the sampling units in a study can be easily ranked than the actual measurement. RSS performs better than simple random sampling (SRS) when the mean of units corresponding to each rank is used. The performance of RSS can be increased further by assigning weights to the ranked observations. In this paper, we propose weighted RSS procedures to estimate the population mean of positively skew distributions. It is shown that the gain in the relative precisions of the population mean for chosen distributions are uniformly higher than those based on RSS. The gains in relative precisions are substantially high. Further, the relative precisions of our estimator are slightly higher than the ones based on Neyman’s optimal allocation model for small sample sizes. Moreover, it is shown that, the performance of the proposed estimator increases as the skewness increases by using the example of lognormal family of distributions.
Keywords
rdered observations; Neyman’s allocation; Relative precision; Skewness; Unbiased estimator; Weight
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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