Estimating Gaussian Distribution Parameters Using Rank Regression and comparing them with the maximum likelihood estimators
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Abstract
The representation of data through a Gaussian model allows it to be more flexible, effectively handle distortions, and avoid over-adaptation to the data. This approach helps improve the model's accuracy and understand how outliers impact the accuracy of the distribution parameters estimator.
In this research, a comparison was made between some methods for estimating Gaussian distribution parameters in analyzing the Survival Function using Rank Regression on the dependent variable and then on the independent variable, in addition to the maximum likelihood estimator method in the presence (and absence) of outliers in the distribution data. The mean square error criterion for the estimated parameters and the chi-square goodness-of-fit test were relied upon to compare the three methods through a simulation study for several parameter values and different sample sizes repeated (1000) times, in addition to real data representing the survival time of early breast cancer patients through a program in the MATLAB program designed for this purpose, in addition to the Easy-Fit program. The results of the study showed that the method of maximum likelihood estimators was superior in the absence of outliers in the Gaussian distribution data, while the method of estimating the rank regression on the independent variable was superior in the presence of outliers.
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