  Extreme value analysis in the presence of censoring is receiving much
attention as it has applications in many disciplines, including survival and
reliability studies. Estimation of extreme value index (EVI) is of primary
importance as it is a critical parameter needed in estimating extreme events
such as quantiles and exceedance probabilities. In this paper, we review
several estimators of the extreme value index when data is subject to random
censoring. In addition, four estimators are proposed, one based on the
exponential regression approximation of log spacings, one based on a Zipf
estimator and two based on variants of the moment estimator. The proposed
estimators and the existing ones are compared under the same simulation
conditions. The performance measures for the estimators include confidence
interval length and coverage probability. The simulation results show that no
estimator is universally the best as the estimators depend on the size of the
EVI parameter, percentage of censoring in the right tail and the underlying
distribution. However, certain estimators such as the proposed reduced-bias
estimator and the adapted moment estimator are found to perform well across
most scenarios. Moreover, we present a bootstrap algorithm for obtaining
samples for extreme value analysis in the context of censoring. Some of the
estimators that performed well in the simulation study are illustrated using a
practical dataset from medical research
