scholarly journals Implicit max-stable extremal integrals

Extremes ◽  
2020 ◽  
Author(s):  
D. Kremer
Keyword(s):  
Loss Function ◽  
Open Problem ◽  
Stochastic Integral ◽  
Extreme Values ◽  
Stable Distributions ◽  
Extreme Value ◽  
Point Of View ◽  
Extreme Value Distributions ◽  
Application Point ◽  
Deterministic Function

Abstract Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function f ≥ 0. From an application point of view, one is rather interested in extreme loss events that occur relative to f than in the corresponding extreme values itself. In this context, so-called f -implicit α-Fréchet max-stable distributions arise and have been used to construct independently scattered sup-measures that possess such margins. In this paper we solve an open problem in Goldbach (2016) by developing a stochastic integral of a deterministic function g ≥ 0 with respect to implicit max-stable sup-measures. The resulting theory covers the construction of max-stable extremal integrals (see Stoev and Taqqu Extremes 8, 237–266 (2005)) and, at the same time, reveals striking parallels.

scholarly journals Extreme value distributions for dependent jointly ln,p-symmetrically distributed random variables

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
K. Müller ◽  
W.-D. Richter
Keyword(s):  
Extreme Values ◽  
Random Variables ◽  
Geometric Approach ◽  
Extreme Value ◽  
Symmetric Distribution ◽  
Tail Behavior ◽  
Extreme Value Distributions ◽  
Symmetric Distributions ◽  
Dependent Random Variables ◽  
Elliptically Contoured

AbstractA measure-of-cone representation of skewed continuous ln,p-symmetric distributions, n ∈ N, p > 0, is proved following the geometric approach known for elliptically contoured distributions. On this basis, distributions of extreme values of n dependent random variables are derived if the latter follow a joint continuous ln,p-symmetric distribution. Light, heavy, and extremely far tails as well as tail indices are discussed, and new parameters of multivariate tail behavior are introduced.

scholarly journals False-Alarm Probabilities in Period Searches: Can Extreme-Value Distributions be of Use?

2011 ◽  
Vol 7 (S285) ◽  
pp. 299-300
Author(s):  
Jan Cuypers
Keyword(s):  
Time Series ◽  
False Alarm ◽  
Extreme Values ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
Extreme Values Distribution ◽  
Values Distribution

AbstractResults of simulating false-alarm probabilities in irregularly sampled time series are presented. Relations to well-known expressions and earlier-used criteria are shown and tested for applicability. The use of an extreme-values distribution in this context is investigated.

scholarly journals Estimation of Extreme Values by the Average Conditional Exceedance Rate Method

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
A. Naess ◽  
O. Gaidai ◽  
O. Karpa
Keyword(s):  
Time Series ◽  
Extreme Values ◽  
Practical Interest ◽  
Extreme Value Distribution ◽  
Real Data ◽  
Extreme Value ◽  
Point Of View ◽  
Statistical Dependence ◽  
Sampled Data ◽  
Threshold Method

This paper details a method for extreme value prediction on the basis of a sampled time series. The method is specifically designed to account for statistical dependence between the sampled data points in a precise manner. In fact, if properly used, the new method will provide statistical estimates of the exact extreme value distribution provided by the data in most cases of practical interest. It avoids the problem of having to decluster the data to ensure independence, which is a requisite component in the application of, for example, the standard peaks-over-threshold method. The proposed method also targets the use of subasymptotic data to improve prediction accuracy. The method will be demonstrated by application to both synthetic and real data. From a practical point of view, it seems to perform better than the POT and block extremes methods, and, with an appropriate modification, it is directly applicable to nonstationary time series.

scholarly journals INITIAL RESEARCH OF MINERAL BASED ANTI-CORROSION MULTICOMPONENT COMPOSITE MATERIAL

2019 ◽  
Vol 48 (05) ◽  
pp. 142-147
Author(s):  
Emil Asgarov
Keyword(s):  
Composite Material ◽  
Extreme Values ◽  
Extreme Value ◽  
Point Of View ◽  
Protective Film ◽  
Weak Point ◽  
Variable Function ◽  
New Material ◽  
Film Layer ◽  
Multicomponent Composite

The new approach is to create a multicomponent composite material on a basis of mineral component by defining extreme value of the multi-variable function. It is decided to carry out theoretical analyze first. For theoretical analysis, the effects of component quantity on the parameters to be determined by experiments and in all cases the results to be theorized. Thus, the mathematical formula for the relation of anti-corrosion with components has been determined. In order to evaluate anti-corrosion it is defined multi-variablefunctional relation and with this function it is achieved extreme values on optimum values of each component. The new material is compared to traditional anti –corrosion material that are common. Currently implemented anti –corrosion material doesn’t require needs of modern technological expectation. From this point of view anti-corrosion materials need to have appropriate technical parameters. Traditional anti-corrosion materials basically have one or two components and these materials has protective film layer. Disadvantage of this film layer is whole layer can easily be destructed from weak point. This is due to the fact that traditional materials form film layer in connection areas. Compare with this one the new material has discrete structure. On this basis, the combination of protective and constructive material binding based on adhesion and cohesion. The structure not allows material to be destructed from weak point. On a basis of achieved theoretical results optimal quantity of each component is clarified, anti-corrosion material is made and tested. The novelty of the approach is to achieve high quality anti-corrosion material by defining an extreme value of the multi-variable function.

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