Performance of Some Robust Estimators for the Weibull Distribution

In this study, we consider some of univariate quantile-based robust estimators. We focus on the estimators such as median, interquartile range, quartile and octile skewness for the Weibull distribution which is one of the most widely applied probability function because of its versatility and relative simplicity. It is important to use robust estimators as a measure of distribution properties for analyzing data in the case of contamination with outliers. For small data sets, it is reported that by introducing kernel estimation for smoothing empirical distribution function, a reduction in mean square error of estimator is achieved by Fernholz (1997) and Hubert et al. (2013). In kernel estimation, it is well known that bandwidth selection is more important than selection of kernel density since bandwidth controls the smoothness of the estimated distribution function. Using simulation studies, we examine some quantile-based estimators for the Weibull distribution with various sample size. The performance of estimators is measured by mean squared error under Different outlier contaminated data. We applied this idea in the case of real data