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A Better Estimator of Population Mean with Power Transformation Based on Ranked Set Sampling

100%
Mehta (Ranka) N., Mandowara V. L.
Statistics in Transition new series
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2012
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vol. 13
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issue 3
551-558
EN
Ranked set sampling (RSS) was first suggested by McIntyre (1952) to increase the efficiency of estimate of the population mean. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). There has been considerable development and many modifications were done on this method. This paper presents a modified ratio estimator using prior value of coefficient of kurtosis of an auxiliary variable x, with the intention to improve the efficiency of ratio estimator in ranked set sampling. The first order approximation to the bias and mean square error (MSE) of the proposed estimator are obtained. A generalized version of the suggested estimator by applying the Power transformation is also presented.
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Two-stage cluster sampling with unequal probability sampling in the first stage and ranked set sampling in the second stage

88%
Ugwu M. C., Madukaife M. S.
Statistics in Transition new series
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2022
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vol. 23
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issue 3
199-214
EN
In this research work we introduce a new sampling design, namely a two-stage cluster sampling, where probability proportional to size with replacement is used in the first stage unit and ranked set sampling in the second in order to address the issue of marked variability in the sizes of population units concerned with first stage sampling. We obtained an unbiased estimator of the population mean and total, as well as the variance of the mean estimator. We calculated the relative efficiency of the new sampling design to the two-stage cluster sampling with simple random sampling in the first stage and ranked set sampling in the second stage. The results demonstrated that the new sampling design is more efficient than the competing design when a significant variation is observed in the first stage units.
3
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On the improvement of paired ranked set sampling to estimate population mean

88%
Rehman S. A., Shabbir J.
Statistics in Transition new series
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2021
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vol. 22
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issue 3
193-205
EN
In ecological and environmental sampling the quantification of units is either difficult or overly demanding in terms of the time, money, workload, it requires. For this reason efficient and cost-effective sampling methods need to be devised for data collecting. The most commonly used method for this purpose is the Ranked Set Sampling (RSS). In this paper, a sampling scheme called Improved Paired Ranked Set Sampling (IPRSS) is proposed to estimate the population mean. The performance of the proposed IPRSS is evaluated under perfect and imperfect rankings. A simulation study based on selected hypothetical distributions and a real-life data set showed that IPRSS is more precise than RSS, Paired RSS (PRSS) or Extreme RSS (ERSS).
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