The Variances of VaR for the Poisson-Gumbel Compound Extreme Value Distribution and for the Poisson-Generalized Pareto Compound Peaks over Threshold Distribution

2009 ◽  
Author(s):  
Yueli Han ◽  
Daoji Shi
Keyword(s):  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Peaks Over Threshold ◽  
Generalized Pareto ◽  
Threshold Distribution

Rate of convergence for the generalized Pareto approximation of the excesses

2003 ◽  
Vol 35 (04) ◽  
pp. 1007-1027 ◽  
Author(s):  
J.-P. Raoult ◽  
R. Worms
Keyword(s):  
Distribution Function ◽  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Generalized Pareto

Let F be a distribution function in the domain of attraction of an extreme-value distribution H γ. If F u is the distribution function of the excesses over u and G γ the distribution function of the generalized Pareto distribution, then it is well known that F u (x) converges to G γ(x/σ(u)) as u tends to the end point of F, where σ is an appropriate normalizing function. We study the rate of (uniform) convergence to 0 of F̅ u (x)-G̅γ((x+u-α(u))/σ(u)), where α and σ are two appropriate normalizing functions.

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.

Rate of convergence for the generalized Pareto approximation of the excesses

2003 ◽  
Vol 35 (4) ◽  
pp. 1007-1027 ◽  
Author(s):  
J.-P. Raoult ◽  
R. Worms
Keyword(s):  
Distribution Function ◽  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Generalized Pareto

Let F be a distribution function in the domain of attraction of an extreme-value distribution Hγ. If Fu is the distribution function of the excesses over u and Gγ the distribution function of the generalized Pareto distribution, then it is well known that Fu(x) converges to Gγ(x/σ(u)) as u tends to the end point of F, where σ is an appropriate normalizing function. We study the rate of (uniform) convergence to 0 of F̅u(x)-G̅γ((x+u-α(u))/σ(u)), where α and σ are two appropriate normalizing functions.

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.

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.

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