A note on Statistics of Extremes for censoring schemes on a heavy right tail

In Statistics of Extremes the most common assumption on any set of univariate data is to consider that we are in the presence of a complete sample. However, in the analysis of some physical phenomena such as wind speed, earthquake intensity or floods, extreme measurements are sometimes not available because of damage in the instruments. Also, in the analysis of lifetime data or reliability data, observations are usually censored. We shall give here special attention to the estimation of a positive extreme value index (EV I), under random censoring. Under such a scheme, any EVI-estimator, the basis for the estimation of all other parameters of extreme events, needs to be slightly modified in order to be consistent. We shall make use of a minimum-variance reduced-bias estimator, valid for heavy right tails, i.e. for a positive EVI. The mixed-moment estimator, valid for a general tail, out of the scope of this paper, is also considered for a comparative study. We shall apply the methodology to survival data sets available in the literature, as well as to simulated data.