Using extreme value theory to estimate large percentiles

Weissman (1978) suggested percentile estimators based on the joint limiting distribution of the k largest order statistics. The present work identifies situations where Weissman's estimators are a significant improvement over the usual sample percentile estimators and gives practical advice on how to use these new estimators effectively. In particular, large reductions in mean squared error can be made when the tails of the distributions are approximately exponential and p ≥ .95.