Estimation of the Reliability Function of the Maxwell - Boltzmann Distribution Using the M-Robust Estimation Methods and Comparing them With Conventional Methods

To achieve the best possible outcomes. The reliability function estimation was also established for the In this study, the scal parameter Maxwell distribution was estimated using both traditional and robust methods, and the results were compared typical estimation methods, which included the Maximum Likelihood method (MLE), the moments method (MOM), and the M- robust method The results were compared using the mean error squared (MSE). The M-robust technique was found to have the lowest mean square error across all sample sizes, as demonstrated by the findings hence, it is regarded as being more effective than the conventional estimate methods. In addition, it was determined that the statistical criterion, also known as MSE, is the most effective way for estimating, and thus, the results of the simulation are based on this. m-strong technique is used to determine the model values (M-strong). According to statistical theory the number of small and medium-sized enterprises (SMEs) decreases as the sample size increases. Because parameter estimates are significantly hindered when the data set has few outliers, m is the method of estimation that is the most reliable. Because of this robust estimation is an essential method for evaluating databases that contain problematic outliers Numerous robust regression estimators as well as M method estimators, are available in a wide variety. The least squares approach is one of the safest methods because of its remarkable efficiency in obtaining the possibilities.