Weibull regression model is one of the most prevalently used parametric regression models. Estimation of the parameters of this model is affected by the presence of outliers. Outliers may be caused by actual rare events or by measurement, coding, or data entry errors, which cause a serious problem in parameter estimation. Therefore, robust estimation methods are used to overcome this problem since they are insensitive to perturbations. This paper discusses the efficiency of using two robust estimation methods, the M-estimation method and the MM-estimation method for estimating the parameters of Weibull regression model. Also, a Monte Carlo simulation study was conducted to compare the performance of robust M-estimation and MM-estimation methods with the maximum likelihood method for estimating the parameters of Weibull regression model in the presence of outliers. The simulation results showed that the robust MM-estimation method gives better performance than the maximum likelihood method and the M-estimation method.
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