Comparison Estimators of Reliability for the Modified Inverse Rayleigh Distribution With Application

This paper aims to derive point estimation formulas for the two parameters of the modified inverse Rayleigh distribution using five estimation methods: Least squares, Cramer–Von Mises, maximum likelihood, White’s, and the New White’s method. A simulation study was conducted to generate samples for three distinct cases based on varying default parameter values and sample sizes. The mean squared error criterion was employed to evaluate the performance of the estimators. The simulation findings demonstrate that the New White’s method is the most efficient across all three cases. Furthermore, the estimators’ formulas were applied to real data obtained from the Kut Textile Factory (General Company for Textile Industries) in Iraq. Parameter estimates and the reliability function were calculated using the five methods. The reliability functions were plotted for each method, and the empirical results aligned with the simulation findings, confirming that the New White’s reliability estimate provides the highest degree of accuracy.