Statistical Extrapolation of Extreme Value Data Based on the Peaks Over Threshold Method

1998 ◽  
Vol 120 (2) ◽  
pp. 91-96 ◽  
Author(s):  
A. Naess
Keyword(s):  
Weibull Distribution ◽  
Return Period ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Environmental Loads ◽  
Estimation Process ◽  
Design Values

This paper discusses the use of the peaks over threshold method for estimating long return period design values of environmental loads. Attention is focused on the results concerning the type of asymptotic extreme value distribution for use in the extrapolation to required design values obtained by such methods, which in many cases seem to indicate that the Weibull distribution for maxima is the appropriate one. It will be shown by a closer scrutiny of the underlying estimation process that very often such a conclusion cannot in fact be substantiated.

scholarly journals Data Geometry and Extreme Value Distribution

2021 ◽  
Vol 2 (2) ◽  
pp. 06-15
Author(s):  
Mamadou Cisse ◽  
Aliou Diop ◽  
Souleymane Bognini ◽  
Nonvikan Karl-Augustt ALAHASSA
Keyword(s):  
Weibull Distribution ◽  
Extreme Values ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Data System ◽  
Peaks Over Threshold ◽  
Stochastic Graphs ◽  
Block Maxima ◽  
Extreme Values Theory

In extreme values theory, there exist two approaches about data treatment: block maxima and peaks-over-threshold (POT) methods, which take in account data over a fixed value. But, those approaches are limited. We show that if a certain geometry is modeled with stochastic graphs, probabilities computed with Generalized Extreme Value (GEV) Distribution can be deflated. In other words, taking data geometry in account change extremes distribution. Otherwise, it appears that if the density characterizing the states space of data system is uniform, and if the quantile studied is positive, then the Weibull distribution is insensitive to data geometry, when it is an area attraction, and the Fréchet distribution becomes the less inflationary.

Extreme Value Statistics of Wind Speed Data by the POT and AER Methods

2008 ◽  
Author(s):  
A. Naess ◽  
E. Haug
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
New Method ◽  
Extreme Value Statistics ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Wind Speed Data

The paper describes a new method for predicting the appropriate extreme value distribution derived from an observed time series. The method is based on introducing a cascade of conditioning approximations to the exact extreme value distribution. This allows for a rational way of capturing dependence effects in the time series. The performance of the method is compared with that of the peaks over threshold method.

Extreme Value Statistics of Wind Speed Data by the POT and ACER Methods

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
A. Naess ◽  
E. Haug
Keyword(s):  
Time Series ◽  
Wind Speed ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Peaks Over Threshold ◽  
Threshold Method ◽  
Wind Speed Data ◽  
Novel Method

The paper describes a novel method for predicting the appropriate extreme value distribution derived from an observed time series. The method is based on introducing a cascade of conditioning approximations to the exact extreme value distribution. This allows for a rational way of capturing dependence effects in the time series. The performance of the method is compared with that of the peaks-over-threshold method.

scholarly journals Interval Estimation for Extreme Value Parameter with Censored Data

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Eun-Joo Lee ◽  
Dane Walker ◽  
David Elliott ◽  
Katlyn Mathy ◽  
Seung-Hwan Lee
Keyword(s):  
Weibull Distribution ◽  
Censored Data ◽  
Interval Estimation ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Finite Sample ◽  
Real World Data ◽  
Scale Parameters ◽  
Statistical Inferences

The Weibull distribution is widely used in the parametric analysis of lifetime data. In place of the Weibull distribution, it is often more convenient to work with the equivalent extreme value distribution, which is the logarithm of the Weibull distribution. The main advantage in working with the extreme value distribution is that unlike the Weibull distribution, the extreme value distribution has location and scale parameters. This paper is devoted to a discussion of statistical inferences for the extreme value distribution with censored data. Numerical simulations are performed to examine the finite sample behaviors of the estimators of the parameters. These procedures are then applied to real-world data.

scholarly journals Extreme Storm Surge estimation and projection through the Metastatistical Extreme Value Distribution

2021 ◽  
Author(s):  
Maria Francesca Caruso ◽  
Marco Marani
Keyword(s):  
Time Series ◽  
Sea Level ◽  
Return Period ◽  
Extreme Value Distribution ◽  
Storm Surges ◽  
Extreme Value ◽  
Value Distribution ◽  
Sample Sizes ◽  
Sea Levels ◽  
Calibration Sample

Abstract. Accurate estimates of the probability of extreme sea levels are pivotal for assessing risk and the design of coastal defense structures. This probability is typically estimated by modelling observed sea-level records using one of a few statistical approaches. In this study we comparatively apply the Generalized Extreme Value (GEV) distribution, based on Block Maxima (BM) and Peak-Over-Threshold (POT) formulations, and the recently Metastatistical Extreme Value Distribution (MEVD) to four long time series of sea-level observations distributed along European coastlines. A cross-validation approach, dividing available data in separate calibration and test sub-samples, is used to compare their performances in high-quantile estimation. To address the limitations posed by the length of the observational time series, we quantify the estimation uncertainty associated with different calibration sample sizes, from 5 to 30 years. Focusing on events with a high return period, we find that the GEV-based approaches and MEVD perform similarly when considering short samples (5 years), while the MEVD estimates outperform the traditional methods when longer calibration sample sizes (10-30 years) are considered. We then investigate the influence of sea-level rise through 2100 on storm surges frequencies. The projections indicate an increase in the height of storm surges for a fixed return period that are spatially heterogeneous across the coastal locations explored.

The Extreme Value Distribution and Application of Decarburization of Piston Rod

2021 ◽  
Vol 105 ◽  
pp. 125-133
Author(s):  
Jin Zhe Chen ◽  
Ge Ping Bi
Keyword(s):  
Parameter Estimation ◽  
Data Collection ◽  
Return Period ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Maximum Depth ◽  
Value Prediction ◽  
Maximum Value

Gumbel extreme value distribution is used to predict the maximum depth of decarburization of piston rod. The results show that: 1) The prediction maximum depth of decarburization of piston rod should include four steps: data collection, parameter estimation, distribution test and maximum value prediction. 2) The maximum depth of decarburization of piston rod consistent with Gumbel minimum distribution. 3) When the return period is 1000, the predicted maximum depth of decarburization is (0.12 ± 0.01) mm, (k = 2).

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