Journal of Statistics Applications & Probability

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The use of ranked set sampling (RSS), a unique and cost-effective sampling technique, is appropriate when determining units is simple and straightforward. The estimates based on RSS are more effective than the conventional unconstrained sampling approaches, and in recent years, their modified versions have gained popularity because of their remarkably increased effectiveness in research projects on forest management. In light of this, the current study was conducted on skewed and unskewed distributions to assess the efficacy of the various modified versions of RSS. Simulated data was produced in R Studio (version 4.1.2 – 2021) using skewed and unskewed probability distributions like the gamma, exponential, uniform, and normal distributions to fulfil the specified goals. In accordance with this, a ranked set sample of sizes 150, 300, 450, 600, 750, 900, 1050, and 1200 with a set size of 3, 6, 9, 12, 15, 18, and 24 using a constant cycle (r) of 50 was drawn from the simulated data using various modified RSS techniques, including: Extreme ranked set sampling (ERSS), Median ranked set sampling (MRSS), Percentile rank set sampling (PRSS), Balanced grouped ranked set sampling (BGRSS), Balanced grouped ranked set sampling (BGRSS), and Truncation based rank set sampling (TBRSS)by means of library( RS Sampling) of R Studio. Since these samples are based on modified versions of RSS that are more regularly spaced and induce stratification at the sample level, which involves a gain in efficiency, it can be seen from the results that modified versions of RSS performed better in unskewed distributions in comparison to skewed distributions in terms of efficiency. Additionally, it was discovered that the effectiveness of every modified RSS algorithm rises as the sample size does. According to empirical research using simulated data, truncation-based rank set sampling (TBRSS), among the modified RSS methods, outperformed its competitors in terms of efficiency. The value of AIC & BIC reduced as the set size across the modified RSS methods increased, according to the goodness of fit results, showing that less information is lost as set size increases. Finally, it can be said that RSS has practical ramifications, and that R packages greatly aid in the implementation of modified RSS methods, which are quite informative and suitable to sample surveys.

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