A tale of two stations: a note on rejecting the Gumbel distribution

• Autorzy: Rydén Jesper

Identyfikatory

DOI

10.1007/s11600-022-00852-1

• Języki publikacji: EN

Abstrakty

EN

The existence of an upper limit for extremes of quantities in the earth sciences, e.g. for river discharge or wind speed, is sometimes suggested. Estimated parameters in extreme-value distributions can assist in interpreting the behaviour of the system. Using simulation, this study investigated how sample size influences the results of statistical tests and related interpretations. Commonly used estimation techniques (maximum likelihood and probability-weighted moments) were employed in a case study; the results were applied in judging time series of annual maximum river flow from two stations on the same river, but with different lengths of observation records. The results revealed that sample size is crucial for determining the existence of an upper bound.

Słowa kluczowe

EN

extreme values; river discharge; GEV distribution; sample size; bootstrap

PL

wartości ekstremalne; wypływ rzeki; dystrybucja GEV; wielkość próbki; bootstrap

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2023
• Tom: Vol. 71, no. 1
• Strony: 385--390
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Rydén Jesper

• Swedish University of Agricultural Sciences, Uppsala, Sweden

• https://orcid.org/0000-0002-5451-4563

Bibliografia

• 1. Bucher A, Segers J (2017) On the maximum likelihood estimator for the generalized extreme-value distribution. Extremes 20:839–872. https://doi.org/10.1007/s10687-017-0292-6
• 2. Cai Y, Hames D (2010) Minimum sample size determination for generalized extreme value distribution. Commun Stat Simul Comput 40(1):87–98. https://doi.org/10.1080/03610918.2010.530368
• 3. Caires S (2007) Extreme wave statistics: confidence intervals. Report prepared for Rijkswaterstaat, Rijksinstituut voor Kust en Zee (RIKZ). http://resolver.tudelft.nl/uuid:8d38ef9c-ead4-4b9d-850c-d4dd2e71a34f
• 4. Canty A, Ripley B (2021) boot: Bootstrap R (S-Plus) Functions. R package version 1.3-28
• 5. Coles SG, Dixon MJ (1999) Likelihood-based inference for extreme value models. Extremes 2:5–23. https://doi.org/10.1023/A:1009905222644
• 6. Coles S, Simiu E (2003) Estimating uncertainty in the extreme value analysis of data generated by a hurricane simulation model. J Engrg Mech 129:1288–1294. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:11(1288)
• 7. Davison AC, Hinkley DV (1997) Bootstrap methods and their applications. Cambridge University Press, Cambridge. 0-521-57391-2. https://doi.org/10.1017/CBO9780511802843
• 8. Dey D, Roy D, Yan J (2016) Univariate extreme value analysis. In extreme value modeling and risk analysis. Methods and applications. CRC Press, Chapman & Hall, Boca Raton. https://doi.org/10.1201/b19721
• 9. Gilleland E (2020) Bootstrap methods for statistical inference. Part II: extreme-value analysis. J Atmos Ocean Technol 37:2135–2144. https://doi.org/10.1175/JTECH-D-20-0070.1
• 10. Gilleland E, Katz, RW (2016) extRemes 2.0: An extreme value analysis package in r. journal of statistical software 72(8), 1–39. https://doi.org/10.18637/jss.v072.i08
• 11. Gumbel EJ (1958) Statistics of extremes. Columbia University Press, New York. https://doi.org/10.7312/gumb92958
• 12. Harris I (2005) Generalised Pareto methods for wind extremes. Useful tool or mathematical mirage? J Wind Eng Ind Aerodyn 93(5):341-360. https://doi.org/10.1016/j.jweia.2005.02.004
• 13. Hosking JRM (2019) L-Moments. R package, version 2.8. https://CRAN.R-project.org/package=lmom
• 14. Hosking JRM, Wallis JR, Wood EF (1985) Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27(3):251–261. https://doi.org/10.2307/1269706
• 15. R Core Team (2021) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/
• 16. Roden GI (1967) On river discharge into the northeastern Pacific Ocean and the Bering Sea. J Geophys Res 72(22):5613–5629. https://doi.org/10.1029/JZ072i022p05613
• 17. Rydén J (2019) A note on analysis of extreme minimum temperatures with the GAMLSS framework. Acta Geophys 67:1599–1604. https://doi.org/10.1007/s11600-019-00363-6
• 18. Rydén J (2022a) Tales of the Wakeby tail and alternatives when modelling extreme floods. REVSTAT—Statistical Journal. https://revstat.ine.pt/index.php/REVSTAT/article/view/454 (accepted)
• 19. Rydén J (2022b) Statistical analysis of possible trends for extreme floods in northern Sweden. River Res Appl. https://doi.org/10.1002/rra.3980 (accepted)
• 20. Simiu E (2007) Discussion: Generalized Pareto methods for wind extremes. Useful tool or mathematical mirage? by Ian Harris. J Wind Eng Ind Aerodyn 95(2):133-136. https://doi.org/10.1016/j.jweia.2006.05.002
• 21. Smith RL (1985) Maximum likelihood estimation in a class of nonregular cases. Biometrika 72:67–90. https://doi.org/10.2307/2336336
• 22. de Vriend HJ, Kok M, Pol J, Hegnauer M (2017) Is there a maximum discharge for the Rhine at Lobith? A publication of the Expertisenetwerk Waterveiligheid. URL: https://www.enwinfo.nl/publish/pages/183541/is-there-a-maximum-discharge-for-the-rhine-at-lobith-march2017.pdf

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).