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In extreme value analysis, the extreme value index plays a vital role as it determines the tail heaviness of the underlying distribution and is the primary parameter required for the estimation of other extreme events. In this paper, we review the estimation of the extreme value index when observations are subject to right random censoring and the presence of covariate information. In addition, we propose some estimators of the extreme value index, including a maximum likelihood estimator from a perturbed Pareto distribution. The existing estimators and the proposed ones are compared through a simulation study under identical conditions. The results show that the performance of the estimators depend on the percentage of censoring, the underlying distribution, the size of extreme value index and the number of top order statistics. Overall, we found the proposed estimator from the perturbed Pareto distribution to be robust to censoring, size of the extreme value index and the number of top order statistics.

A Simulation Comparison of Estimators of Conditional Extreme Value Index under Right Random Censoring