Abstract

In the presence of censored data, selecting an appropriate estimation method is critical for obtaining reliable parameter estimates. This thesis compares the performance of the parametric maximum likelihood estimator (MLE) and a modified, semi-parametric MLE under random censoring. The comparison focuses on estimator of variance, mean squared error, and confidence regions, using theoretical derivations and simulation studies. We examine various combinations of continuous distributions for the event and censoring variables, including Exponential, Weibull, Gamma, Beta, and Pareto models. Our findings show that the modified estimator performs comparably to or better than the parametric estimator, particularly at low censoring rates and for specific distributional configurations. In cases with high censoring, the parametric estimator largely yielded lower variances. These results provide practical guidance for applied statisticians working with randomly censored data, especially in fields such as medical research, reliability engineering, and finance.