Parameter Estimation for the Transmuted Inverse Rayleigh Distribution Using Ranked Set Sampling: Applications and Analysis

This paper examines various estimation methods for the parameters of the transmuted inverse Rayleigh distribution (TIRD) using both ranked set sampling (RSS) and simple random sampling (SRS) designs. The parameters are estimated using maximum likelihood estimation, ordinary and weighted least squares, and the maximum product of spacings. Additionally, five goodness-of-fit estimators are evaluated: Anderson-Darling (AD), right-tail AD, left-tail AD, left-tail second-order, and the Cram?er-von Mises estimator. A comprehensive simulation study is conducted to assess the performance of these estimators while ensuring an equal number of observations across both sampling designs. Furthermore, an analysis of a real COVID-19 dataset belonging to the Netherlands of 30 days, which is fitted both numerically and graphically to the TIRD, demonstrates the practical applicability of the proposed estimation methods. The results show that RSS-based estimators consistently outperform their SRS counterparts in terms of mean squared error, bias, and mean absolute relative error across all methods. The findings highlight the advantages of RSS for parameter estimation in the TIRD, demonstrating its superiority over SRS for statistical inference. In particular, RSS proves to be more effective when dealing with small sample sizes.