Robust estimation methods for estimating distributional parameters

The most commonly used methods in the estimation of distributional parameters are the maximum likelihood and moments estimators. However, it is well-known that these estimators can be very unreliable in the case of outliers in the data. The objective of this thesis is examination of the robust estimators, which are used in the estimation of distributional parameters, in the case of outliers in the data. The considered robust estimators are given as follow: robust estimators for the linear regression model, the estimator based on quantiles, the robust estimators for transformed location-scale family, the method of medians, the method of trimmed moments. The considered robust estimators are also obtained for estimating the parameters of the Weibull and Pareto distributions and the performance of the considered robust estimators are evaluated via a simulation study for the case of outliers and non-outliers in data. Also, the considered estimators are applied on two real life data and the obtained results are discussed.