Premium
Dutch case studies of the estimation of extreme quantiles and associated uncertainty by bootstrap simulations
Author(s) -
Pandey M. D.,
Van Gelder P. H. A. J. M.,
Vrijling J. K.
Publication year - 2004
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.656
Subject(s) - quantile , generalized pareto distribution , econometrics , statistics , pareto principle , parametric statistics , extreme value theory , estimation , variance (accounting) , pareto distribution , series (stratigraphy) , computer science , mathematics , economics , paleontology , management , accounting , biology
The article presents several practical applications of the peaks‐over‐threshold (POT) method to the estimation of extreme quantiles of environmental variables, such as sea level, river discharge, precipitation, wave height and earthquake magnitude using actual data collected in the Netherlands. The quantile estimation by the POT method is conceptually simple, since it involves fitting a Pareto distribution to peaks of a time series exceeding a high threshold. However, practical applications of the POT method are confounded by the selection of a suitable threshold, since quantile estimates tend to exhibit large and erratic variation with threshold. The article illustrates this threshold sensitivity of quantile estimates in a variety of data sets. Specifically, the article compares the performance of L‐moment and de Haan methods for modelling peak data by the Pareto distribution. To evaluate the quantile bias and variance as functions of threshold, a semi‐parametric bootstrap algorithm is utilized. The article deliberately emphasizes the use of conceptually simple and practical methods to promote engineering applications of statistical theory of extremes. Copyright © 2004 John Wiley & Sons, Ltd.