Study on New Ratio and Product Type Estimators for Population Mean Under Ranked Set Sampling

Objectives: The study deals with the concept of Ranked Set Sampling (RSS) as an effective measure to find out the mean of the population when a sample of small size can be found without measuring or with other methods like ranking. The primary goal of this study is to investigate how well the proposed estimators perform compared to existing estimators. Methods: This study has introduced new ratio and product estimators to see the population mean under ranked set sampling and compare them with the existing ones in terms of Mean Square Error (MSE) and efficiency. Findings: The optimum value of the modified estimators is obtained. The proposed estimators are better than the existing estimators, such as the mean per unit estimator, ratio estimator, and product estimator in ranked set sampling. We have used bivariate normal distribution through the ranked set sampling technique, and the proposed estimators' relative efficiency is higher. Novelty: Two tables are used to show the comparison between the proposed estimator and the existing estimators by using bivariate normal distribution. Empirical studies using simulations further validate the effectiveness of these new estimators, suggesting their potential for broader application in statistical analysis. Keywords: Estimators, Population, Mean Square Error, Efficiency, Ranked Set Sampling