Efficiency of double ranked set sampling for the power-function distribution

This study investigates the efficiency of Ranked Set Sampling (RSS) and Double Ranked Set Sampling (DRSS) in estimating the population mean under the Power-Function distribution. Building upon the framework of Simple Random Sampling (SRS), exact analytical expressions for the mean and variance of the corresponding estimators are derived. Comparative analyses across various sample sizes (m = 2, 3, and 5) reveal that DRSS consistently outperforms both RSS and SRS by achieving substantial variance reduction. Furthermore, the concept of perfect ranking is revisited, and exact expressions for the probability of perfect ranking are obtained for both sampling schemes. The findings emphasize the superior precision and practical advantages of DRSS, particularly for small and moderate sample sizes, without increasing the measurement effort.