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In this study, we compare the three different methods for the joint estimation of both scale and shape parameters for two-parameter in Weibull distribution when data are contaminated with outliers: the method of moment (MOM), the maximum likelihood method (MLE) and the weighted likelihood method (WLE). The performance of these methods is compared using the Monte Carlo s imulation and the efficiency of these methods is compared based on RMSE. From simulation results, we found that the WLE outperforms the other methods for the scale parameter in term of RMSE of the estimator for scale parameter for . For the RMSE of the estimator for shape parameter of the MLE approach provides better results for the scale parameter when outliers in the data set are small. In term of RMSE for two parameter estimators, the WLE performs better than the other methods when . For and 1.5, the MOM also performs well, especially and outliers in the data set are small.
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