The estimation of extreme quantiles of wind velocity using L-moments in the peaks-over-threshold approach

2001 ◽  
Vol 23 (2) ◽  
pp. 179-192 ◽  
Author(s):  
M.D Pandey ◽  
P.H.A.J.M Van Gelder ◽  
J.K Vrijling
Keyword(s):  
Wind Velocity ◽  
Peaks Over Threshold ◽  
Extreme Quantiles ◽  
L Moments ◽  
Threshold Approach

Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events

2014 ◽  
Vol 46 (02) ◽  
pp. 478-495 ◽  
Author(s):  
Sebastian Engelke ◽  
Alexander Malinowski ◽  
Marco Oesting ◽  
Martin Schlather
Keyword(s):  
Stable Process ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Shape Functions ◽  
Peaks Over Threshold ◽  
New Methods ◽  
Convergence Results ◽  
Block Maxima ◽  
Threshold Approach ◽  
Mixed Moving Maxima

In this paper we provide the basis for new methods of inference for max-stable processes ξ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process η in the max-domain of attraction of ξ on being extremal, several convergence results for the increments of η are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events η. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified.

scholarly journals Fatigue analysis of a bridge deck using the peaks-over-threshold approach with application to the Millau viaduct

2020 ◽  
Vol 2 (8) ◽  
Author(s):  
Mariia Nesterova ◽  
Franziska Schmidt ◽  
Christian Soize
Keyword(s):  
Fatigue Damage ◽  
Extreme Values ◽  
Initial Distribution ◽  
Linear Extrapolation ◽  
Peaks Over Threshold ◽  
Innovative Method ◽  
Structural Details ◽  
Load Effects ◽  
Existing Bridges ◽  
Threshold Approach

AbstractUsually, to estimate the fatigue life of structural details in existing bridges, fatigue damage assessed with monitoring data is extrapolated linearly in time. In this study, a methodology is proposed for predicting the numbers of fatigue cycles with the peaks-over-threshold approach. On the other side, this POT approach, which is based on extreme values, is, as usually, also used to predict the load effects of extreme amplitude. This provides an innovative method to predict fatigue damage, which considers the initial distribution of numbers of cycles over time. It may account for traffic growth in volume and mass. This paper shows the comparison between reliability indexes assessed with the proposed method and the linear extrapolation.

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