scholarly journals Predictability of extreme values in geophysical models

2012 ◽  
Vol 19 (5) ◽  
pp. 529-539 ◽  
Author(s):  
A. E. Sterk ◽  
M. P. Holland ◽  
P. Rabassa ◽  
H. W. Broer ◽  
R. Vitolo
Keyword(s):  
Extreme Value Theory ◽  
Finite Time ◽  
Lead Time ◽  
Extreme Values ◽  
Initial Conditions ◽  
Value Theory ◽  
Wind Speeds ◽  
Finite Time Lyapunov Exponents ◽  
Deterministic Systems ◽  
Time Predictability

Abstract. Extreme value theory in deterministic systems is concerned with unlikely large (or small) values of an observable evaluated along evolutions of the system. In this paper we study the finite-time predictability of extreme values, such as convection, energy, and wind speeds, in three geophysical models. We study whether finite-time Lyapunov exponents are larger or smaller for initial conditions leading to extremes. General statements on whether extreme values are better or less predictable are not possible: the predictability of extreme values depends on the observable, the attractor of the system, and the prediction lead time.

scholarly journals THE FULL TAILS GAMMA DISTRIBUTION APPLIED TO MODEL EXTREME VALUES

2017 ◽  
Vol 47 (3) ◽  
pp. 895-917 ◽  
Author(s):  
Joan del Castillo ◽  
Jalila Daoudi ◽  
Isabel Serra
Keyword(s):  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Extreme Values ◽  
Dispersion Model ◽  
Value Theory ◽  
Quantitative Modelling ◽  
Exponential Distributions ◽  
Exponential Dispersion Model ◽  
Aggregate Loss ◽  
Very High

AbstractIn this paper, we introduce the simplest exponential dispersion model containing the Pareto and exponential distributions. In this way, we obtain distributions with support (0, ∞) that in a long interval are equivalent to the Pareto distribution; however, for very high values, decrease like the exponential. This model is useful for solving relevant problems that arise in the practical use of extreme value theory. The results are applied to two real examples, the first of these on the analysis of aggregate loss distributions associated to the quantitative modelling of operational risk. The second example shows that the new model improves adjustments to the destructive power of hurricanes, which are among the major causes of insurance losses worldwide.

scholarly journals The Potential Wind Power Resource in Central-South of the Constanta County

2019 ◽  
Vol 15 (3) ◽  
pp. 1-12
Author(s):  
Emilian Boboc
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Extreme Values ◽  
Reanalysis Data ◽  
Value Theory ◽  
Physical Models ◽  
Structural Safety ◽  
Energy Yield ◽  
Wind Speeds ◽  
Mean Wind Speed

Abstract Usually, wind turbine generator’s structures or radio masts are located in wind exposed sites. The paper aims to investigate the wind conditions in the nearby area of Cobadin Commune, Constanta County, Romania at heights of 150-200m above the surface using global reanalysis data sets CFSR, ERA 5, ERA I and MERRA 2. Using the extreme value theory and the physical models of the datasets, the research focuses on the assessment of the maximum values that are expected for the wind speeds, but the wind statistics created can be used for a further wind or energy yield calculation. Without reaching the survival wind speed for wind turbine generators, with mean wind speed values higher than 7 m/s and considering the cut-in and cut-out wind speeds of 3 m/s, respectively 25 m/s, the site can be exploited in more than 90% of the time to generate electricity, thus, the paper is addressed to the investors in the energy of renewable sources. At the same time, the insights of the wind characteristics and the knowledge of the extreme values of the wind speed can be useful, not just for the designers, in the rational assessment of the structural safety of wind turbines, but also those evaluating the insured losses.

Frequentist and Bayesian extreme value analysis on the wildfire events in Greece

2020 ◽  
Author(s):  
Nikos Koutsias ◽  
Frank A. Coutelieris
Keyword(s):  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Burned Area ◽  
Accurate Assessment ◽  
Peaks Over Threshold ◽  
Bayesian Approaches ◽  
Value Analysis

<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>

Extreme values of non-stationary random sequences

1986 ◽  
Vol 23 (04) ◽  
pp. 937-950 ◽  
Author(s):  
Jürg Hüsler
Keyword(s):  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extremal Index ◽  
Stationary Case ◽  
Random Sequences ◽  
Similar Role ◽  
High Level

We extend some results of the extreme-value theory of stationary random sequences to non-stationary random sequences. The extremal index, defined in the stationary case, plays a similar role in the extended case. The details show that this index describes not only the behaviour of exceedances above a high level but also above a non-constant high boundary.

Domains of Attraction for an Autoparametric Mass-Pendulum System: A Lyapunov Exponent Map Approach

2003 ◽  
Author(s):  
Khalid El-Rifai ◽  
George Haller ◽  
Anil K. Bajaj
Keyword(s):  
Lyapunov Exponent ◽  
Finite Time ◽  
Initial Conditions ◽  
Transient Behavior ◽  
System Response ◽  
Pendulum System ◽  
Domains Of Attraction ◽  
Nonlinear Dynamical ◽  
Finite Time Lyapunov Exponents ◽  
Finite Time Lyapunov Exponent

Many recent studies have been performed on resonantly excited mass-pendulum systems with autoparametric (internal) resonance capturing interesting local steady state phenomena. The objective of this work is to explore the transient behavior in such systems. The domains of attraction of the time-periodic system provide some help in understanding the transient dynamics, and these are sought using a recently developed algorithm that solves for the finite-time Lyapunov exponent over a grid of initial conditions. Though the use of finite-time Lyapunov exponents in nonlinear dynamical analyses is not novel, its application to multi-degree-offreedom forced nonlinear systems has not been reported in the literature. In addition to identifying regions of different final states, the technique used captures different levels of attraction within a domain. This sheds some light on the role played by other modes present in a multi-degree-of-freedom system in shaping the overall system response.

scholarly journals Extreme Value Theory and Large Fire Losses

1974 ◽  
Vol 7 (3) ◽  
pp. 293-310 ◽  
Author(s):  
G. Ramachandran
Keyword(s):  
Statistical Theory ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Large Fire ◽  
Fire Insurance ◽  
Reinsurance Treaty

The statistical theory of extreme values well described by Gumbel [1] has been fruitfully applied in many fields, but only in recent times has it been suggested in connection with fire insurance problems. The idea originally stemmed from a consideration of the ECOMOR reinsurance treaty proposed by Thepaut [2]. Thereafter, a few papers appeared investigating the usefulness of the theory in the calculation of an excess of loss premium. Among these, Beard [3, 4], d'Hooge [5] and Jung [6] have made contributions which are worth studying. They have considered, however, only the largest claims during a succession of periods. In this paper, generalized techniques are presented which enable use to be made of all large losses that are available for analysis and not merely the largest. These methods would be particularly useful in situations where data are available only for large losses.

scholarly journals An Application of Extreme Value Theory to Learning Analytics: Predicting Collaboration Outcome from Eye-tracking Data

2017 ◽  
Vol 4 (3) ◽  
Author(s):  
Kshitij Sharma ◽  
Valérie Chavez-Demoulin ◽  
Pierre Dillenbourg
Keyword(s):  
Eye Tracking ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Collaborative Problem Solving ◽  
Tracking Data ◽  
Previous Approach ◽  
The Mean

The statistics used in education research are based on central trends such as the mean or standard deviation, discarding outliers. This paper adopts another viewpoint that has emerged in Statistics, called the Extreme Value Theory (EVT). EVT claims that the bulk of the normal distribution is mostly comprised of uninteresting variations while the most extreme values convey more information. We applied EVT to eye-tracking data collected during online collaborative problem solving with the aim of predicting the quality of collaboration. We compare our previous approach, based on central trends, with an EVT approach focused on extreme episodes of collaboration. The latter occurred to provide a better prediction of the quality of collaboration.

scholarly journals Hidden Strange Nonchaotic Attractors

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 652
Author(s):  
Marius-F. Danca ◽  
Nikolay Kuznetsov
Keyword(s):  
Finite Time ◽  
Initial Conditions ◽  
Power Spectra ◽  
Recurrence Plot ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
Hidden Attractor ◽  
Test Power ◽  
Finite Time Lyapunov Exponents ◽  
Strange Nonchaotic Attractors

In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the considered hidden strange nonchaotic attractor, a self-excited chaotic attractor and a quasiperiodic attractor of the Rabinovich–Fabrikant system are comparatively analyzed.

scholarly journals Maximum Values of Frozen Soil’s Depth and Hoar Frost’s Thickness Estimated on the Basis of Extreme Values Theory

2018 ◽  
Vol 12 (2) ◽  
pp. 13-23
Author(s):  
Maria Nedealcov ◽  
Valentin Răileanu ◽  
Gheorghe Croitoru ◽  
Cojocari Rodica ◽  
Crivova Olga
Keyword(s):  
Risk Factors ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Gumbel Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Frozen Soil ◽  
Return Interval ◽  
The Mean ◽  
Extreme Values Theory

Abstract Extreme climatic phenomena present risk factors for agriculture, health, constructions, etc. and are studied profoundly these past years using extreme value theory. Several relation that describe positive extreme values’ probability Generalized Extreme Value and Gumbel distribution are presented in the article. As a example, we show the maps of characteristic and reference values of the maximum depth of the frozen soil and thickness of hoar-frost with a probability of exceeding per year equal to 0,02, which is equivalent to the mean return interval of 50 years. The obtained results could serve as a base for elaboration of national annexes in constructions.

Predictions of Extreme Values of Significant Wave Height

2003 ◽  
Author(s):  
C. Guedes Soares ◽  
R. G. Ferreira ◽  
Manuel G. Scotto
Keyword(s):  
Extreme Value Theory ◽  
Significant Wave Height ◽  
Extreme Values ◽  
Value Theory ◽  
Environmental Data ◽  
Threshold Method ◽  
Peak Over Threshold ◽  
Peak Over Threshold Method ◽  
Low Probability ◽  
Quantile Estimates

This paper provides an overview of different methods of extrapolating environmental data to low probability levels based on the extreme value theory. It discusses the Annual Maxima method and the Peak Over Threshold method, using unified terminology and notation. Furthermore, it describes a method based on the r largest order statistics that has the advantage of providing more accurate parameters and quantile estimates than the Annual Maxima method. Several examples illustrate the methodology and reveal strengths and weaknesses of the various approaches.

Sign in / Sign up

Export Citation Format

Share Document