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 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.

scholarly journals Characterizing the Variability and Extremes of the Stratospheric Polar Vortices Using 2D Moment Analysis

2011 ◽  
Vol 68 (6) ◽  
pp. 1194-1213 ◽  
Author(s):  
Daniel M. Mitchell ◽  
Andrew J. Charlton-Perez ◽  
Lesley J. Gray
Keyword(s):  
Extreme Value Theory ◽  
Planetary Wave ◽  
Value Theory ◽  
Extreme Value ◽  
Moment Analysis ◽  
Analysis Tool ◽  
Sudden Stratospheric Warming ◽  
Extreme Variability ◽  
The Mean ◽  
The Moment

Abstract The mean state, variability, and extreme variability of the stratospheric polar vortices, with an emphasis on the Northern Hemisphere (NH) vortex, are examined using two-dimensional moment analysis and extreme value theory (EVT). The use of moments as an analysis tool gives rise to information about the vortex area, centroid latitude, aspect ratio, and kurtosis. The application of EVT to these moment-derived quantities allows the extreme variability of the vortex to be assessed. The data used for this study are 40-yr ECMWF Re-Analysis (ERA-40) potential vorticity fields on interpolated isentropic surfaces that range from 450 to 1450 K. Analyses show that the most extreme vortex variability occurs most commonly in late January and early February, consistent with when most planetary wave driving from the troposphere is observed. Composites around sudden stratospheric warming (SSW) events reveal that the moment diagnostics evolve in statistically different ways between vortex splitting events and vortex displacement events, in contrast to the traditional diagnostics. Histograms of the vortex diagnostics on the 850-K (~10 hPa) surface over the 1958–2001 period are fitted with parametric distributions and show that SSW events constitute the majority of data in the tails of the distributions. The distribution of each diagnostic is computed on various surfaces throughout the depth of the stratosphere; it shows that in general the vortex becomes more circular with higher filamentation at the upper levels. The Northern and Southern Hemisphere (SH) vortices are also compared through the analysis of their respective vortex diagnostics, confirming that the SH vortex is less variable and lacks extreme events compared to the NH vortex. Finally, extreme value theory is used to statistically model the vortex diagnostics and make inferences about the underlying dynamics of the polar vortices.

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.

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 Topics in data analysis using R in extreme value theory

2013 ◽  
Vol 10 (1) ◽  
Author(s):  
Helena Penalva ◽  
Manuela Neves
Keyword(s):  
Applied Sciences ◽  
Data Analysis ◽  
Open Source Software ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Data Sets ◽  
Statistics Of Extremes

The statistical Extreme Value Theory has grown gradually from the beginning of the 20th century. Its unquestionable importance in applications was definitely recognized after Gumbel's book in 1958, Statistics of Extremes. Nowadays there is a wide number of applied sciences where extreme value statistics are largely used. So, accurately modeling extreme events has become more and more important and the analysis requires tools that must be simple to use but also should consider complex statistical models in order to produce valid inferences. To deal with accurate, friendly, free and open-source software is of great value for practitioners and researchers. This paper presents a review of the main steps for initializing a data analysis of extreme values in R environment. Some well documented packages are briefly described and two data sets will be considered for illustrating the use of some functions.

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.

Extreme values of non-stationary random sequences

1986 ◽  
Vol 23 (4) ◽  
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.

scholarly journals A Method for Estimation of Extreme Values of Wind Pressure on Buildings Based on the Generalized Extreme-Value Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Yong Quan ◽  
Fei Wang ◽  
Ming Gu
Keyword(s):  
Extreme Value Theory ◽  
Present Method ◽  
Extreme Values ◽  
Time History ◽  
Value Theory ◽  
Extreme Value ◽  
Wind Pressure ◽  
Probability Density Distribution ◽  
Generalized Extreme Value ◽  
Building Model

By analysis of statistical characteristics and probability density distribution of extreme values of wind pressures on the surfaces of a typical low-rise building model and a typical high-rise building model, characteristics of the commonly used methods for estimating the extreme-values of wind pressure are discussed. The relationship between the parameters of the extreme value distribution of wind pressure and its observation length is then deduced based on the generalized extreme value theory and the independence of the observed extreme values. A new method for estimating the extreme values is developed by dividing the time history sample of the wind pressure into several subsamples. The extreme values of the wind pressure coefficients calculated with the present method and those with the commonly used methods are compared and the results indicate that the present method can estimate the extreme values of non-Gaussian wind pressure more accurately than the commonly used ones.

scholarly journals USING EXTREME VALUE THEORY TO IDENTIFY RAILCAR ASYMMETRIC WHEEL WEAR AND ITS BENEFIT ANALYSIS

Transport ◽  
2019 ◽  
Vol 34 (5) ◽  
pp. 569-578
Author(s):  
Yu Cui ◽  
Qing He ◽  
Zhenhua Zhang ◽  
Zhiguo Li
Keyword(s):  
Extreme Value Theory ◽  
Extreme Values ◽  
Early Stage ◽  
Cost Effective ◽  
Value Theory ◽  
Extreme Value ◽  
Skewed Distribution ◽  
Wheel Wear ◽  
Monetary Benefit ◽  
Elliptically Contoured

Railcar asymmetric wheel wear leads to severe wear on one wheel but mild wear on the other wheel. The consequences of the asymmetric wheel include accelerated wear, mechanical failure and downtime, and high financial penalties. Therefore, identifying the asymmetric wheel wear is critical not only for cost effective maintenance but also for safe operations. Fortunately, the increasing amount of various wayside detectors is instrumented along the railway that can monitor the health of railcar components and log plenty of detailed information about railroad operations. One can use this information to identify the asymmetric wheel wear in the early stage. However, most elliptically contoured distributions are effective in describing normal events but not in dealing with the outliers, which mainly locate in the tails of the distribution. Asymmetric wheel wear requires effective anomaly detection that mainly focuses on the extreme values in the tail of a right-skewed distribution. In this paper, we employ the Extreme Value Theory (EVT), which handles the unusually high or low data in the distribution, to derive an extreme value score to identify asymmetric wheel wear. Experiment results show that identification of asymmetric wheel wear can generate huge monetary benefit in terms of reducing average maintenance times of railcars.

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