Weighted Likelihood Estimator of Scale Parameter for the Two-parameter Weibull Distribution with a Contamination

Abstract

In this article, we propose weighted likelihood estimator (WLE) that assigns zero
weights to observations with small likelihood. We also examine the robustness properties of the maximum likelihood estimator (MLE) and WLE for the scale parameter of the twoparameter Weibull distribution when the data set has a contamination. We investigated the performance of the WLE as compared to the MLE and found that the WLE outperforms the MLE with respect to the relative bias and quadratic risk values.