scholarly journals Extreme value statistics of correlated random variables: A pedagogical review

2020 ◽  
Vol 840 ◽  
pp. 1-32 ◽  
Author(s):  
Satya N. Majumdar ◽  
Arnab Pal ◽  
Grégory Schehr
Keyword(s):  
Random Variables ◽  
Extreme Value ◽  
Extreme Value Statistics

scholarly journals GLOBAL FLUCTUATIONS IN PHYSICAL SYSTEMS: A SUBTLE INTERPLAY BETWEEN SUM AND EXTREME VALUE STATISTICS

2008 ◽  
Vol 22 (20) ◽  
pp. 3311-3368 ◽  
Author(s):  
MAXIME CLUSEL ◽  
ERIC BERTIN
Keyword(s):  
Extreme Values ◽  
Random Variables ◽  
Extreme Value ◽  
Physical Models ◽  
Extreme Value Statistics ◽  
Specific Class ◽  
Qualitative Properties ◽  
Rigorous Results ◽  
General Mapping ◽  
Global Fluctuations

Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of global quantities, in a direct or indirect way. This review discusses different connections that may appear between problems of sums and of extreme values of random variables, and emphasizes physical situations in which such connections are relevant. Along this line of thought, standard convergence theorems for sums and extreme values of independent and identically distributed random variables are recalled, and some rigorous results as well as more heuristic reasonings are presented for correlated or non-identically distributed random variables. More specifically, the role of extreme values within sums of broadly distributed variables is addressed, and a general mapping between extreme values and sums is presented, allowing us to identify a class of correlated random variables whose sum follows (generalized) extreme value distributions. Possible applications of this specific class of random variables are illustrated on the example of two simple physical models. A few extensions to other related classes of random variables sharing similar qualitative properties are also briefly discussed, in connection with the so-called BHP distribution.

On the locations of maxima and minima in a sequence of exchangeable random variables

2021 ◽  
Vol 105 (0) ◽  
pp. 35-50
Author(s):  
D. Ferger
Keyword(s):  
Infinite Sequence ◽  
Random Variables ◽  
Finite Sequence ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Classical Approach ◽  
Linear Transformations ◽  
Exchangeable Random Variables

We show for a finite sequence of exchangeable random variables that the locations of the maximum and minimum are independent from every symmetric event. In particular they are uniformly distributed on the grid without the diagonal. Moreover, for an infinite sequence we show that the extrema and their locations are asymptotically independent. Here, in contrast to the classical approach we do not use affine-linear transformations. Moreover it is shown how the new transformations can be used in extreme value statistics.

On the spectral shape of SEP events: An extreme value statistics approach

2013 ◽  
Author(s):  
M. Laurenza ◽  
G. Consolini ◽  
M. Storini ◽  
A. Damiani
Keyword(s):  
Extreme Value ◽  
Spectral Shape ◽  
Extreme Value Statistics

scholarly journals Bestimmung seltener Starkniederschläge kurzer Dauer - Fallbeispiele im Vergleich mit den schweizerischen Starkniederschlagskarten | Determination of Rare Rainfall Intensities of Short-Duration - Case Studies Compared with Maps of Intense Rainfall in Switzerland

1999 ◽  
Vol 150 (6) ◽  
pp. 209-218 ◽  
Author(s):  
Felix Forster ◽  
Walter Baumgartner
Keyword(s):  
Case Studies ◽  
Short Duration ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Intense Rainfall

The two maps of intense rainfall in the Hydrological Atlas of Switzerland (1992, 1997) are compared to data of an evaluation of extreme value statistics. The results are transferred to recommendations for practioners.

scholarly journals Evaluation of Fatigue Characteristics of Aluminum Alloys and Mechanical Components Using Extreme Value Statistics and C-specimens

Metals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1915
Author(s):  
Jungsub Lee ◽  
Sang-Youn Park ◽  
Byoung-Ho Choi
Keyword(s):  
Aluminum Alloys ◽  
Fem Analysis ◽  
Extreme Value ◽  
Fatigue Tests ◽  
Extreme Value Statistics ◽  
Fatigue Properties ◽  
Chemical Compositions ◽  
Cross Sectional ◽  
Fatigue Characteristics ◽  
Mechanical Components

In this study, the fatigue characteristics of aluminum alloys and mechanical components were investigated. To evaluate the effect of forging, fatigue specimens with the same chemical compositions were prepared from billets and forged mechanical components. To evaluate the cleanliness of the aluminum alloys, the cross-sectional area of specimens was observed, and the maximum inclusion sizes were obtained using extreme value statistics. Rotary bending fatigue tests were performed, and the fracture surfaces of the specimens were analyzed. The results show that the forging process not only elevated the fatigue strength but also reduced the scatter of the fatigue life of aluminum alloys. The fatigue characteristics of C-specimens were obtained to develop finite-element method (FEM) models. With the intrinsic fatigue properties and strain–life approach, the FEM analysis results agreed well with the test results.

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