Some hydrological applications of small sample estimators of Generalized Pareto and Extreme Value distributions C. De Michele a, * , G. Salvadori a,b a DIIAR (Sezione Idraulica), Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy b Dipartimento di Matematica ‘Ennio De Giorgi’, Universita ` di Lecce, Provinciale Lecce-Arnesano, P.O. Box 193, I-73100 Lecce, Italy Received 3 December 2002; revised 10 June 2004; accepted 15 June 2004 Abstract The Generalized Pareto (GP) and Generalized Extreme Value (GEV) distributions have been widely applied in the frequency analysis of numerous meteorological and hydrological events. There are several techniques for the estimation of the parameters, which use the total sample as a source of information. In this paper, we show how valuable estimates are also possible considering only a proper subset of the sample, and we identify the portion of the sample containing the most relevant information for estimating a given parameter. In turn, this may prevent the use of anomalous values, which may adversely affect standard techniques. Here, we illustrate original techniques (based on linear combinations of ‘selected’ order statistics) to estimate the position parameter, the scale parameter, the quantiles, and the possible scaling behavior of the GP and GEV distributions with negative shape parameters. These estimators are generally unbiased and Mean-Square-Error-consistent. In addition, weakly consistent estimators of quantiles are introduced, the calculation of which does not require the knowledge of any parameter. Some case studies illustrate the applicability of the new techniques in hydrologic practice, and comparisons with standard methods are presented. The new estimators proposed may provide a reasonable alternative to standard methods, and may serve, at least, as a methodology to cross-check the estimates resulting from the application of other techniques. q 2004 Elsevier B.V. All rights reserved. Keywords: Linear estimator; Generalized Extreme Value distribution; Generalized Pareto distribution; Order statistics; Position/scale parameter; Scaling 1. Introduction The Generalized Extreme Value (GEV) distri- bution, introduced by Jenkinson (1955), provides a general framework for the frequency analysis of extreme meteorological and hydrological events. Such a statistical model has been widely used in the analysis of hydrological extremes because of its flexibility in representing the three asymptotic types of extreme value probability distributions, first introduced by Gnedenko (1943) and further refined by Gumbel (1954). For example, the GEV distribution was selected to model extreme flows in the pioneering 0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2004.06.015 Journal of Hydrology 301 (2005) 37–53 www.elsevier.com/locate/jhydrol * Corresponding author. Tel.: C39-02-2399-6233; fax: C39-02- 2399-6207. E-mail addresses: carlo.demichele@polimi.it (C. De Michele), gianfausto.salvadori@unile.it (G. Salvadori).