Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis / Modèles d’extrêmes utilisant le système Burr XII étendu à trois paramètres et application à l’analyse fréquentielle des crues

Abstract

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
• distribution Burr XII étendue
• analyse fréquentielle de crues
• distribution de Pareto généralisée
• distribution asymptotique
• distribution log-logistique
• distribution de Pareto
• distribution de Weibull

Additional information

Notes on contributors

Quanxi Shao

[email protected]