69
Views
4
CrossRef citations to date
0
Altmetric
Research Papers

The importance of statistical uncertainties in selecting appropriate methods for estimation of extremes

Pages 99-107 | Received 02 Apr 2007, Accepted 20 Dec 2007, Published online: 23 Aug 2010

References

  • Shannon , C.E. 1948 . “A Mathematical Theory of Communication” . Bell Systems Technical Journal , 27 : 379 – 423 . 623 – 656 .
  • D'Agostino , R.B. and Stephens , M.A. 1986 . Goodness of Fit Techniques , Dekker .
  • Robert , C. 2005 . The Bayesian Choice , Springer Texts in Statistics .
  • Chevalier , M. , Perez , D. , Biasse , J.‐M. and Mitterand , J.‐M. 1997 . “Resampling and Simulation on Small‐Size Samples” . In Advances in Safety & Reliability , Edited by: Guedes Soares , C. Pergamon .
  • Devictor , N. , Chapuliot , S. and Eid , M. “Monte‐Carlo Simulation to Assess Structures Reliability” . Proceedings of Esrel'99 . Edinburgh.
  • Pickands , J. 1975 . “Statistical Inference using Extreme Order Statistics” . The Annals of Statistics , 3 : 119 – 131 .
  • Diebolt , J. , Garrido , M. and Trottier , C. 2001 . A Bayesian Regularization Procedure for a Better Extremal Fit , INRIA Research Report
  • Gnedenko , B. 1943 . “Sur la Distribution limite du terme maximum d'une série aléatoire” . Annals of Mathematics, Second Series , 44 : 423 – 453 .
  • Castillo , E. 1988 . Extreme Value Theory in Engineering , Academic Press Inc. .
  • Weibull , W. 1961 . Fatigue Testing and Analysis of Results , London : Pergamon .
  • Scarf , P.A. and Laycock , P.J. 1996 . “Estimation of Extremes in Corrosion Engineering” . Journal of Applied Statistics , 23 (6) : 621 – 643 .
  • Lindley , D.V. 1983 . “Reconciliation of Probability Distributions” . Operations Research , 31 : 866 – 880 .
  • Perreault , L. , Bobée , B. and Rasmussen , P.F. 1999 . “Halphen Distribution System. I: Mathematical and Statistical Properties” . Journal of Hydrologic Engineering , 4 (3) : 189 – 196 .
  • Perreault , L. , Bobée , B. and Rasmussen , P.F. 1999 . “Halphen Distribution System. II: Parameter and Quantile Estimation” . Journal of Hydrologic Engineering , 4 (3) : 200 – 208 .
  • van Gelder , P.H.A.J.M. 2000 . “Statistical Methods for the Risk‐Based Design of Civil Structures” . Communications on Hydraulic and Geotechnical Engineering . TU Delft
  • Garrido , M. 2002 . “TU‐0753 ‐ Modélisation des événements rares et estimation des quantiles extrêmes, méthodes de sélection de modèles pour les queues de distribution” . Thèse de : Grenoble , 1 : 231 12 juin 2002 ‐ Document en français; Titre anglais : “Modelling of Rare Events and Estimation of Extreme Quantiles, Model Selecting Methods for Distribution Tails”
  • Design Discharges on Dutch Rivers (in Dutch) . 2002 . Report from the Ministry of Water Management. The Boertien Committee Approach to Extrapolation of River Discharges Downloadable from: www.rijkswaterstaat.nl/rws/riza/home/publicaties/rapporten/2002/rr_2002_014.pdf
  • Alexander , M.R. , Bakker , R. and Wim , M.J. 2005 . Luxemburg, Heterogeneous Distributions within Flood Frequency Analysis, ISSH ‐ Stochastic Hydraulics 2005, 23 and 24 May 2005 Nijmegen, , The Netherlands
  • Statistical Software Packages: SAS, Matlab, SPSS, Stagraphics, Splus, Statistica, Backgrounds of these Packages can be Conveniently Found via Internet Search Engines.
  • Anderson , T. W. and Darling , D. A. 1952 . “Asymptotic Theory of Certain ‘Goodness‐of‐Fit’ Criteria Based on Stochastic Processes” . Annals of Mathematical Statistics , 23 : 193 – 212 .
  • Stephens , M.A. 1974 . “EDF Statistics for Goodness of Fit and Some Comparisons” . Journal of the American Statistical Association , 69 : 730 – 737 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.