Extreme values identification in regression using a peaks-over-threshold approach

2014 ◽  
Vol 42 (3) ◽  
pp. 566-576 ◽  
Author(s):  
Tong Siu Tung Wong ◽  
Wai Keung Li
2020 ◽  
Vol 2 (8) ◽  
Author(s):  
Mariia Nesterova ◽  
Franziska Schmidt ◽  
Christian Soize

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.


2014 ◽  
Vol 46 (02) ◽  
pp. 478-495 ◽  
Author(s):  
Sebastian Engelke ◽  
Alexander Malinowski ◽  
Marco Oesting ◽  
Martin Schlather

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.


2020 ◽  
Author(s):  
Nikos Koutsias ◽  
Frank A. Coutelieris

<p>A statistical analysis on the wildfire events, that have taken place in Greece during the period 1985-2007, for the assessment of the extremes has been performed. The total burned area of each fire was considered here as a key variable to express the significance of a given event. The data have been analyzed through the extreme value theory, which has been in general proved a powerful tool for the accurate assessment of the return period of extreme events. Both frequentist and Bayesian approaches have been used for comparison and evaluation purposes. Precisely, the Generalized Extreme Value (GEV) distribution along with Peaks over Threshold (POT) have been compared with the Bayesian Extreme Value modelling. Furthermore, the correlation of the burned area with the potential extreme values for other key parameters (e.g. wind, temperature, humidity, etc.) has been also investigated.</p>


2021 ◽  
Vol 2 (2) ◽  
pp. 06-15
Author(s):  
Mamadou Cisse ◽  
Aliou Diop ◽  
Souleymane Bognini ◽  
Nonvikan Karl-Augustt ALAHASSA

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.


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