A Modified Quantile Estimator Using Extreme-Value Theory with Applications

Reliable predictions by means of quantiles constitute one of the most important tasks not only in statistics but in entire science. Quantiles may be estimated by using Extreme- Value Theory (EVT). However, the properties of many estimators based on this theory depend heavily on the actual location. In this paper modified estimators for the quantiles are derived, the properties of which are less sensitive with respect to location. Moreover, these modified quantile estimators are also symmetric with regard to the mean for symmetric distributions, which is not the case for some of the estimators based on the EVT. The modified quantile estimators are a limiting result of an infinity shift of location of the estimators proposed by Dekkers et al. (The Annals of Statistics 17: 1833-1855, 1989). The results may be used in establishing control limits for Shewhart control charts.