Covariate Extreme Value Analysis Using Wave Spectral Partitioning

2020 ◽  
Vol 37 (5) ◽  
pp. 873-888 ◽  
Author(s):  
Jesús Portilla-Yandún ◽  
Edwin Jácome
Keyword(s):  
Extreme Values ◽  
Wind Waves ◽  
Spectral Energy Distribution ◽  
Wave Spectrum ◽  
Wave Climate ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Spectral Energy ◽  
Value Analysis ◽  
Spectral Partitioning

AbstractAn important requirement in extreme value analysis (EVA) is for the working variable to be identically distributed. However, this is typically not the case in wind waves, because energy components with different origins belong to separate data populations, with different statistical properties. Although this information is available in the wave spectrum, the working variable in EVA is typically the total significant wave height Hs, a parameter that does not contain information of the spectral energy distribution, and therefore does not fulfill this requirement. To gain insight in this aspect, we develop here a covariate EVA application based on spectral partitioning. We observe that in general the total Hs is inappropriate for EVA, leading to potential over- or underestimation of the projected extremes. This is illustrated with three representative cases under significantly different wave climate conditions. It is shown that the covariate analysis provides a meaningful understanding of the individual behavior of the wave components, in regard to the consequences for projecting extreme values.

scholarly journals EXTREME VALUE ANALYSIS WITHOUT THE LARGEST VALUES: WHAT CAN BE DONE?

2019 ◽  
Vol 34 (2) ◽  
pp. 200-220
Author(s):  
Jingjing Zou ◽  
Richard A. Davis ◽  
Gennady Samorodnitsky
Keyword(s):  
Order Statistics ◽  
Extreme Values ◽  
Sample Path ◽  
Estimation Procedure ◽  
Extreme Value ◽  
Hill Estimator ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Heavy Tailed ◽  
The Hill

AbstractIn this paper, we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree distributions of such networks tend to have power law behavior in the tails. We focus on the Hill estimator, which plays a starring role in heavy-tailed modeling. The Hill estimator for these data exhibited a smooth and increasing “sample path” as a function of the number of upper order statistics used in constructing the estimator. This behavior became more apparent as we artificially removed more of the upper order statistics. Building on this observation we introduce a new version of the Hill estimator. It is a function of the number of the upper order statistics used in the estimation, but also depends on the number of unavailable extreme values. We establish functional convergence of the normalized Hill estimator to a Gaussian process. An estimation procedure is developed based on the limit theory to estimate the number of missing extremes and extreme value parameters including the tail index and the bias of Hill's estimator. We illustrate how this approach works in both simulations and real data examples.

scholarly journals Extreme value analysis of wave climate around Farasan Islands, southern Red Sea

2020 ◽  
Vol 207 ◽  
pp. 107395 ◽  
Author(s):  
V.R. Shamji ◽  
V.M. Aboobacker ◽  
T.C. Vineesh
Keyword(s):  
Red Sea ◽  
Wave Climate ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Farasan Islands

scholarly journals Extreme Value Analysis for Time-variable Mixed Workload

2021 ◽  
Author(s):  
Szilárd Bozóki ◽  
András Pataricza
Keyword(s):  
Extreme Values ◽  
Real Life ◽  
Extreme Value ◽  
Time Variable ◽  
Extreme Value Analysis ◽  
Computing Systems ◽  
Value Analysis ◽  
Root Cause ◽  
Extreme Value Theorem ◽  
Dynamic Time

Proper timeliness is vital for a lot of real-world computing systems. Understanding the phenomena of extreme workloads is essential because unhandled, extreme workloads could cause violation of timeliness requirements, service degradation, and even downtime. Extremity can have multiple roots: (1) service requests can naturally produce extreme workloads; (2) bursts could randomly occur on a probabilistic basis in case of a mixed workload in multiservice systems; (3) workload spikes typically happen in deadline bound tasks.Extreme Value Analysis (EVA) is a statistical method for modeling the extremely deviant values corresponding to the largest values. The foundation mathematics of EVA, the Extreme Value Theorem, requires the dataset to be independent and identically distributed. However, this is not generally true in practice because, usually, real-life processes are a mixture of sources with identifiable patterns. For example, seasonality and periodic fluctuations are regularly occurring patterns. Deadlines can be purely periodic, e.g., monthly tax submissions, or time variable, e.g., university homework submission with variable semester time schedules.We propose to preprocess the data using time series decomposition to separate the stochastic process causing extreme values. Moreover, we focus on the case where the root cause of the extreme values is the same mechanism: a deadline. We exploit known deadlines using dynamic time warp to search for the recurring similar workload peak patterns varying in time and amplitude.

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>

scholarly journals Extreme Value Analysis of Dynamical Wave Climate Projections in the Mediterranean Sea

2015 ◽  
Vol 66 ◽  
pp. 210-219 ◽  
Author(s):  
Zacharias G. Kapelonis ◽  
Panagiotis N. Gavriliadis ◽  
Gerassimos A. Athanassoulis
Keyword(s):  
Mediterranean Sea ◽  
Wave Climate ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Climate Projections ◽  
Value Analysis ◽  
The Mediterranean

scholarly journals A Two-Scale Approximation for Efficient Representation of Nonlinear Energy Transfers in a Wind Wave Spectrum. Part II: Application to Observed Wave Spectra

2009 ◽  
Vol 39 (10) ◽  
pp. 2451-2476 ◽  
Author(s):  
William Perrie ◽  
Donald T. Resio
Keyword(s):  
Wind Waves ◽  
Spectral Energy Distribution ◽  
Wave Spectrum ◽  
Field Research ◽  
New Method ◽  
Spectral Energy ◽  
Net Energy ◽  
Wave Spectra ◽  
Spectral Evolution ◽  
Long Distance

Abstract In Part I of this series, a new method for estimating nonlinear transfer rates in wind waves, based on a two-scale approximation (TSA) to the full Boltzmann integral (FBI) for quadruplet wave–wave interactions, was presented, and this new method was tested for idealized spectral data. Here, the focus is on comparisons of the TSA and the discrete interaction approximation (DIA) with the FBI for observed wave spectra from field measurements. Observed wave spectra are taken from a wave gauge array in Currituck Sound and a directional waverider off the coast near the Field Research Facility at Duck, North Carolina. Results show that the TSA compares much more favorably to the FBI than does the DIA, even for cases in which the parametric component of the formulation does not capture the spectral energy distribution very well. These results remain valid for the TSA estimates when the FBI results are significantly affected by the directional distribution of energy. It is also shown that although nonlinear transfers are substantially weaker in swell portions of the spectrum these interactions contribute significantly to the spectral evolution and net energy balance in long-distance swell propagation.

Electro-Mechanical Admittance-Based Damage Detection Using Extreme Value Statistics

2008 ◽  
Vol 385-387 ◽  
pp. 561-564 ◽  
Author(s):  
Costas P. Providakis
Keyword(s):  
Health Monitoring ◽  
Extreme Values ◽  
Simulated Data ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Extreme Value Analysis ◽  
Engineering Structures ◽  
Value Analysis ◽  
Electromechanical Impedance ◽  
Tail Distribution

This paper presents the use of statistically rigorous algorithms combined with electromechanical (E/M) impedance approach for health monitoring of engineering structures. In particular, a statistical pattern recognition procedure is developed, based on frequency domain data of electromechanical impedance, to establish a decision boundary for damage identification. In order to diagnose damage with statistical confidence, health monitoring is cast in the context of outlier detection framework. Inappropriate modeling of tail distribution of outliers imposes potentially misleading behavior associated with damage. The present paper attempts to address the problem of establishing decision boundaries based on extreme value statistics so that the extreme values of outliers associated with tail distribution can be properly modeled. The validity of the proposed method is demonstrated using finite element method (FEM) simulated data while a comparison is performed for the extreme value analysis results contrasted with the standard approach where it is assumed that the damage-sensitive features are normally distributed.

Extreme value analysis of wave climate in Chesapeake Bay

2018 ◽  
Vol 159 ◽  
pp. 22-36 ◽  
Author(s):  
Arash Niroomandi ◽  
Gangfeng Ma ◽  
Xinyu Ye ◽  
Sha Lou ◽  
Pengfei Xue
Keyword(s):  
Chesapeake Bay ◽  
Wave Climate ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis

Uncertainties in Extreme Value Analysis of Wave Climate Data and Wave Climate Projections

2015 ◽  
Author(s):  
Erik Vanem
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Wave Climate ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Climate Projections ◽  
Data Sets ◽  
Climate Data ◽  
Value Analysis ◽  
Significant Wave

The extreme values of climate data are of interest in design of marine structures and the return values of certain met-ocean parameters such as significant wave height is of particular importance. However, there are various ways of analyzing the extremes and estimating the required return values, which introduce additional uncertainties. These are investigated in this paper by applying different methods to particular data sets of significant wave height, corresponding to the historic climate and two future projections of the climate assuming different forcing scenarios. In this way, the uncertainty due to the extreme value analysis can also be compared to the uncertainty due to a changing climate. The different approaches that will be considered is the initial distribution approach, the block maxima approach, the peak over threshold (POT) approach and the average conditional exceedance rate method (ACER). Furthermore, the effect of different modelling choices within each of the approaches will be explored. Thus, a range of different return value estimates for the different data sets is obtained. This exercise reveals that the uncertainty due to the extreme value analysis method is notable and, as expected, the variability of the estimates increases for higher return periods. Moreover, even though the variability due to the extreme value analysis is greater than the climate variability, a shift towards higher extremes in a future wave climate can clearly be discerned in the particular datasets that have been analysed.

scholarly journals Non-stationary Extreme Value Analysis: a simplified approach for Earth science applications

2016 ◽  
Author(s):  
Lorenzo Mentaschi ◽  
Michalis Vousdoukas ◽  
Evangelos Voukouvalas ◽  
Ludovica Sartini ◽  
Luc Feyen ◽  
...  
Keyword(s):  
Time Series ◽  
Extreme Values ◽  
Extreme Value ◽  
Stationary Time Series ◽  
Alternative Methods ◽  
Extreme Value Analysis ◽  
Accurate Estimation ◽  
Residual Water ◽  
Value Analysis ◽  
Simplified Approach

Abstract. Statistical approaches to study extreme events require by definition long time series of data. The climate is subject to natural and anthropogenic variations at different temporal scales, leaving their footprint on the frequency and intensity of climatic and hydrological extremes, therefore assumption of stationarity is violated and alternative methods to conventional stationary Extreme Value Analysis (EVA) need to be adopted. In this study we introduce the Transformed-Stationary (TS) methodology for non-stationary EVA. This approach consists in (i) transforming a non-stationary time series into a stationary one to which the stationary EVA theory can be applied; and (ii) reverse-transforming the result into a non-stationary extreme value distribution. As a transformation we propose and discuss a simple time-varying normalization of the signal and show that it allows a comprehensive formulation of non stationary GEV/GPD models with constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the ones from (a) a stationary EVA on quasi-stationary slices of non stationary series and (b) the previously applied non stationary EVA approach. However, the proposed technique comes with advantages in both cases, as in contrast to (a) it uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels; and with respect to (b) it decouples the detection of non-stationary patterns from the fitting of the extreme values distribution. As a result the steps of the analysis are simplified and intermediate diagnostics are possible. In particular the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on running mean and standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and easy to implement and control. An open-source MATLAB toolbox has been developed to cover this methodology, available at https://bitbucket.org/menta78/tseva.

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