Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis

A new theoretically-based distribution in frequency analysis is proposed. The extended three-parameter Burr XII distribution includes the generalized Pareto distribution, which is used to model the exceedences over threshold; log-logistic distribution, which is also advocated in flood frequency anal...

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Published in:Hydrological sciences journal 2004-08, Vol.49 (4), p.685-702
Main Authors: Shao, Quanxi, Wong, Heung, Xia, Jun, Ip, Wai-Cheung
Format: Article
Language:English
Subjects:
Earth sciences
Earth, ocean, space
Engineering and environment geology. Geothermics
Exact sciences and technology
Freshwater
Hydrology
Hydrology. Hydrogeology
Natural hazards: prediction, damages, etc
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creator Shao, Quanxi
Wong, Heung
Xia, Jun
Ip, Wai-Cheung
description A new theoretically-based distribution in frequency analysis is proposed. The extended three-parameter Burr XII distribution includes the generalized Pareto distribution, which is used to model the exceedences over threshold; log-logistic distribution, which is also advocated in flood frequency analysis; and Weibull distribution, which is a part of the generalized extreme value distribution used to model annual maxima as special cases. The extended Burr distribution is flexible to approximate extreme value distribution. Note that both the generalized Pareto and generalized extreme value distributions are limiting results in modelling the exceedences over threshold and block extremes, respectively. From a modelling perspective, generalization might be necessary in order to obtain a better fit. The extended three-parameter Burr XII distribution is therefore a meaningful candidate distribution in the frequency analysis. Maximum likelihood estimation for this distribution is investigated in the paper. The use of the extended three-parameter Burr XII distribution is demonstrated using data from China.
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subjects Earth sciences
Earth, ocean, space
Engineering and environment geology. Geothermics
Exact sciences and technology
Freshwater
Hydrology
Hydrology. Hydrogeology
Natural hazards: prediction, damages, etc
title Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis
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