Comparing Methods for Estimating Gamma Distribution Parameters with Outliers Observation

Abstract

The purpose of our research is to work to maintain parameters for the Gamma Distribution within a better frame of precision in the context of other methods and dealing with outliers. Outliers are common and pose a threat to modelling because one little outlier scales a statistical model and brings about the estimations of parametric index validity. The objective of this study was to find useful applications for the detection and mitigating effect of outliers accomplished through the Hampel filter, the nonlinear fit of the Gamma distribution using the Median Rank Regression (MRR) method for the calculation of the shape parameter and scale parameters. This study then generated simulated data drawn from various parameter values of the Gamma distribution modelled with outliers and ran through the proposed Hampel-MRR method. These results were compared with those produced by the MLE and classical MRR methods based on MSE performance measures. From this research, it was observed that the proposed method gives a more accurate and robust estimate of the parameters, especially with increasing sample sizes and varying parameter values. Implications of this research are those of broader application for the improvement of reliability research. This is just what is needed in decomposing survivability time distribution aiming to predict system performance and maintenance interventions. Superb empowerment and clubbing the years of theory with real-time applications are big draws for this technique over its counterparts in the midpoint of the era of outliers.