Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/32632
Title: Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis
Authors: Shao, Q
Wong, H 
Xia, J
Ip, WC
Issue Date: 2004
Source: Hydrological sciences journal, 2004, v. 49, no. 4, p. 685-701
Abstract: 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.
Keywords: Extended Burr XII distribution
Flood frequency analysis
Generalized Pareto distribution
Limiting distribution
Log-logistic distribution
Pareto distribution
Weibull distribution
Journal: Hydrological Sciences Journal 
ISSN: 0262-6667
DOI: 10.1623/hysj.49.4.685.54425
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