Estimation methods based on ranked set sampling for the unit Birnbaum-Saunders distribution

A more cost-effective and time-efficient method for data collection is Ranked Set Sampling (RSS), which yields more accurate results compared to the classical Simple Random Sampling (SRS) method. The Unit Birnbaum-Saunders (U-BS) distribution, a newly introduced unit distribution, is particularly useful for analyzing bounded data within the range (0,1). This article focuses examines various estimation techniques for unknown parameters of the U-BS distribution, applied in both RSS and SRS. These techniques include: Maximum Likelihood, Least Squares, Maximum Product of Spacing, Minimum distances and Kolmogorov method. The efficiency and comparison of these techniques are illustrated through a simulation study, where key metrics such as the average estimators, average bias, mean square errors (MSE), and mean relative errors are computed. Additionally, a real-world milk production dataset is analyzed to demonstrate the practical applicability of the proposed estimators. The results from both the simulation and data analysis indicate that RSS is more efficient than SRS for estimating the parameters of the U-BS distribution.