scholarly journals An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails

2021 ◽  
Author(s):  
M. de Carvalho ◽  
S. Pereira ◽  
P. Pereira ◽  
P. de Zea Bermudez
Keyword(s):  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Finite Sample ◽  
Bayesian Lasso ◽  
Proposed Model ◽  
Left And Right ◽  
Heavy Tailed ◽  
The Right ◽  
Type Specification

AbstractWe introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification based on a Lagrangian restriction. Our model can be used to track if some covariates are significant for the lower values, but not for the (right) tail—and vice versa; in addition to this, the proposed model bypasses the need for conditional threshold selection in an extreme value theory framework. We assess the finite-sample performance of the proposed methods through a simulation study that reveals that our method recovers the true conditional distribution over a variety of simulation scenarios, along with being accurate on variable selection. Rainfall data are used to showcase how the proposed method can learn to distinguish between key drivers of moderate rainfall, against those of extreme rainfall. Supplementary materials accompanying this paper appear online.

scholarly journals Return Period Evaluation of the Largest Possible Earthquake Magnitudes in Mainland China Based on Extreme Value Theory

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3519
Author(s):  
Yanbing Bai ◽  
Ning Ma ◽  
Shengwang Meng
Keyword(s):  
Earthquake Engineering ◽  
Return Period ◽  
Extreme Value Theory ◽  
Threshold Model ◽  
Mainland China ◽  
Value Theory ◽  
Extreme Value ◽  
Geographical Information ◽  
Geographical Regions ◽  
The Right

The largest possible earthquake magnitude based on geographical characteristics for a selected return period is required in earthquake engineering, disaster management, and insurance. Ground-based observations combined with statistical analyses may offer new insights into earthquake prediction. In this study, to investigate the seismic characteristics of different geographical regions in detail, clustering was used to provide earthquake zoning for Mainland China based on the geographical features of earthquake events. In combination with geospatial methods, statistical extreme value models and the right-truncated Gutenberg–Richter model were used to analyze the earthquake magnitudes of Mainland China under both clustering and non-clustering. The results demonstrate that the right-truncated peaks-over-threshold model is the relatively optimal statistical model compared with classical extreme value theory models, the estimated return level of which is very close to that of the geographical-based right-truncated Gutenberg–Richter model. Such statistical models can provide a quantitative analysis of the probability of future earthquake risks in China, and geographical information can be integrated to locate the earthquake risk accurately.

scholarly journals Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2208
Author(s):  
Ekaterina Morozova ◽  
Vladimir Panov
Keyword(s):  
Stock Returns ◽  
Mixture Models ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Numerical Examples ◽  
Proposed Model ◽  
Mixing Parameter ◽  
Heavy Tailed ◽  
Regularly Varying Distribution

This paper deals with the extreme value analysis for the triangular arrays which appear when some parameters of the mixture model vary as the number of observations grows. When the mixing parameter is small, it is natural to associate one of the components with “an impurity” (in the case of regularly varying distribution, “heavy-tailed impurity”), which “pollutes” another component. We show that the set of possible limit distributions is much more diverse than in the classical Fisher–Tippett–Gnedenko theorem, and provide the numerical examples showing the efficiency of the proposed model for studying the maximal values of the stock returns.

scholarly journals Extreme value theory in the solar wind: the role of current sheets

2019 ◽  
Vol 490 (2) ◽  
pp. 1879-1893
Author(s):  
Tiago F P Gomes ◽  
Erico L Rempel ◽  
Fernando M Ramos ◽  
Suzana S A Silva ◽  
Pablo R Muñoz
Keyword(s):  
Solar Wind ◽  
Power Spectra ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Intermittent Turbulence ◽  
Current Sheets ◽  
Developed Turbulence ◽  
The Right

ABSTRACT This article provides observational evidence for the direct relation between current sheets, multifractality and fully developed turbulence in the solar wind. In order to study the role of current sheets in extreme-value statistics in the solar wind, the use of magnetic volatility is proposed. The statistical fits of extreme events are based on the peaks-over-threshold (POT) modelling of Cluster 1 magnetic field data. The results reveal that current sheets are the main factor responsible for the behaviour of the tail of the magnetic volatility distributions. In the presence of current sheets, the distributions display a positive shape parameter, which means that the distribution is unbounded in the right tail. Thus the appearance of larger current sheets is to be expected and magnetic reconnection events are more likely to occur. The volatility analysis confirms that current sheets are responsible for the −5/3 Kolmogorov power spectra and the increase in multifractality and non-Gaussianity in solar wind statistics. In the absence of current sheets, the power spectra display a −3/2 Iroshnikov–Kraichnan law. The implications of these findings for the understanding of intermittent turbulence in the solar wind are discussed.

scholarly journals Evaluation of classical spatial-analysis schemes of extreme rainfall

2012 ◽  
Vol 12 (11) ◽  
pp. 3229-3240 ◽  
Author(s):  
D. Ceresetti ◽  
E. Ursu ◽  
J. Carreau ◽  
S. Anquetin ◽  
J. D. Creutin ◽  
...  
Keyword(s):  
Cross Validation ◽  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Optimal Interpolation ◽  
Peaks Over Threshold ◽  
Model Block ◽  
Block Maxima ◽  
Extreme Value Model ◽  
Value Model

Abstract. Extreme rainfall is classically estimated using raingauge data at raingauge locations. An important related issue is to assess return levels of extreme rainfall at ungauged sites. Classical methods consist in interpolating extreme-value models. In this paper, such methods are referred to as regionalization schemes. Our goal is to evaluate three classical regionalization schemes. Each scheme consists of an extreme-value model (block maxima, peaks over threshold) taken from extreme-value theory plus a method to interpolate the parameters of the statistical model throughout the Cévennes-Vivarais region. From the interpolated parameters, the 100-yr quantile level can be estimated over this whole region. A reference regionalization scheme is made of the couple block maxima/kriging, where kriging is an optimal interpolation method. The two other schemes differ from the reference by replacing either the extreme-value model block maxima by peaks over threshold or kriging by a neural network interpolation procedure. Hyper-parameters are selected by cross-validation and the three regionalization schemes are compared by double cross-validation. Our evaluation criteria are based on the ability to interpolate the 100-yr return level both in terms of precision and spatial distribution. It turns out that the best results are obtained by the regionalization scheme combining the peaks-over-threshold method with kriging.

scholarly journals Extreme Value Theory Applied to r Largest Order Statistics Under the Bayesian Approach

2019 ◽  
Vol 42 (2) ◽  
pp. 143-166 ◽  
Author(s):  
Renato Santos Silva ◽  
Fernando Ferraz Nascimento
Keyword(s):  
Monte Carlo ◽  
Order Statistics ◽  
Bayesian Approach ◽  
Extreme Value Theory ◽  
Likelihood Estimation ◽  
Value Theory ◽  
Extreme Value ◽  
Environmental Data ◽  
Heavy Tailed ◽  
The Bayesian Approach

Extreme Value Theory (EVT) is an important tool to predict efficient gains and losses. Its main areas of analyses are economic and environmental. Initially, for that form of event, it was developed the use of patterns of parametric distribution such as Normal and Gamma. However, economic and environmental data presents, in most cases, a heavy-tailed distribution, in contrast to those distributions. Thus, it was faced a great difficult to frame extreme events. Furthermore, it was almost impossible to use conventional models, making predictions about non-observed events, which exceed the maximum of observations. In some situations EVT is used to analyse only the maximum of some dataset, which provide few observations, and in those cases it is more effective to use the r largest-order statistics. This paper aims to propose Bayesian estimators' for parameters of the r largest-order statistics. During the research, it was used Monte Carlo simulation to analyze the data, and it was observed some properties of those estimators, such as mean, variance, bias and Root Mean Square Error (RMSE). The estimation of the parameters provided inference for its parameters and return levels. This paper also shows a procedure to the choice of the r-optimal to the r largest-order statistics, based on the Bayesian approach applying Markov chains Monte Carlo (MCMC). Simulation results reveal that the Bayesian approach has a similar performance to the Maximum Likelihood Estimation, and the applications were developed using the Bayesian approach and showed a gain in accurary compared with otherestimators.

scholarly journals Analysis of extreme rainfall in Oti River Basin (West Africa)

2021 ◽  
Author(s):  
Komi S. Klassou ◽  
Kossi Komi
Keyword(s):  
River Basin ◽  
Heavy Rainfall ◽  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Return Periods ◽  
Maximum Rainfall ◽  
Daily Data ◽  
Dry Spell ◽  
Annual Maximum Rainfall

Abstract Understanding how extreme rainfall is changing locally is a useful step in the implementation of efficient adaptation strategies to negative impacts of climate change. This study aims to analyze extreme rainfall over the middle Oti River Basin. Ten moderate extreme precipitation indices as well as heavy rainfall of higher return periods (25, 50, 75, and 100 years) were calculated using observed daily data from 1921 to 2018. In addition, Mann–Kendall and Sen's slope tests were used for trend analysis. The results showed decreasing trends in most of the heavy rainfall indices while the dry spell index exhibited a rising trend in a large portion of the study area. The occurrence of heavy rainfall of higher return periods has slightly decreased in a large part of the study area. Also, analysis of the annual maximum rainfall revealed that the generalized extreme value is the most appropriate three-parameter frequency distribution for predicting extreme rainfall in the Oti River Basin. The novelty of this study lies in the combination of both descriptive indices and extreme value theory in the analysis of extreme rainfall in a data-scarce river basin. The results are useful for water resources management in this area.

scholarly journals Introducing Non-Stationarity Into the Development of Intensity-Duration-Frequency Curves under a Changing Climate

Water ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1008
Author(s):  
Daniele Feitoza Silva ◽  
Slobodan P. Simonovic ◽  
Andre Schardong ◽  
Joel Avruch Goldenfum
Keyword(s):  
Return Period ◽  
Climate Models ◽  
Global Climate ◽  
Extreme Rainfall ◽  
Value Theory ◽  
Extreme Value ◽  
Global Climate Models ◽  
Water Infrastructure ◽  
Planning And Design ◽  
Intensity Duration Frequency

Intensity-duration-frequency (IDF) relationships are traditional tools in water infrastructure planning and design. IDFs are developed under a stationarity assumption which may not be realistic, neither in the present nor in the future, under a changing climatic condition. This paper introduces a framework for generating non-stationary IDFs under climate change, assuming that probability of occurrence of quantiles changes over time. Using Extreme Value Theory, eight trend combinations in Generalized Extreme Value (GEV) parameters using time as covariate are compared with a stationary GEV, to identify the best alternative. Additionally, a modified Equidistance Quantile Matching (EQMNS) method is implemented to develop IDFs for future conditions, introducing non-stationarity where justified, based on the Global Climate Models (GCM). The methodology is applied for Moncton and Shearwater gauges in Northeast Canada. From the results, it is observed that EQMNS is able to capture the trends in the present and to translate them to estimated future rainfall intensities. Comparison of present and future IDFs strongly suggest that return period can be reduced by more than 50 years in the estimates of future rainfall intensities (e.g., historical 100-yr return period extreme rainfall may have frequency smaller than 50-yr under future conditions), raising attention to emerging risks to water infrastructure systems.

Using Extreme Value Theory to Model Electricity Price Risk with an Application to the Alberta Power Market

2005 ◽  
Vol 23 (5) ◽  
pp. 375-403 ◽  
Author(s):  
W. D. Walls ◽  
Wei. Zhang
Keyword(s):  
Extreme Value Theory ◽  
Value At Risk ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Financial Assets ◽  
Historical Simulation ◽  
Generalized Pareto ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

Value-at-risk (VaR) is a measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR has become a standard measure of market risk and a common practice is to compute VaR by assuming that changes in value of the portfolio are conditionally normally distributed. However, assets returns usually come from heavy-tailed distributions, so computing VaR under the assumption of conditional normality can be an important source of error. We illustrate in our application to competitive electric power prices in Alberta, Canada, that VaR estimates based on extreme value theory models, in particular the generalized Pareto distribution are, more accurate than those produced by alternative models such as normality or historical simulation.

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