Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions

 Ad hoc techniques for estimating the quantiles of the Generalized Pareto (GP) and the Generalized Extreme Values (GEV) distributions are introduced. The estimators proposed are based on new estimators of the position and the scale parameters recently introduced in the Literature. They provide valuable estimates of the quantiles of interest both when the shape parameter is known and when it is unknown (this latter case being of great relevance in practical applications). In addition, weakly-consistent estimators are introduced, whose calculation does not require the knowledge of any parameter. The procedures are tested on simulated data, and comparisons with other techniques are shown. The research was partially supported by Contract n. ENV4-CT97-0529 within the project “FRAMEWORK” of the European Community – D.G. XII. Grants by “Progetto Giovani Ricercatori” are also acknowledged.