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.

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 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 Optimization of Parameters in the Generalized Extreme-Value Distribution Type 1 for Three Populations Using Harmonic Search

Atmosphere ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 257 ◽  
Author(s):  
Juan Pablo Molina-Aguilar ◽  
Alfonso Gutierrez-Lopez ◽  
Jose Angel Raynal-Villaseñor ◽  
Luis Gabriel Garcia-Valenzuela
Keyword(s):  
Extreme Values ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Distribution Functions ◽  
Value Distribution ◽  
Generalized Extreme Value Distribution ◽  
Type I ◽  
Generalized Extreme Value ◽  
Heuristic Technique ◽  
Distribution Type

Due to its geographical position, Mexico is exposed annually to cold fronts and tropical cyclones, registering extremely high values that are atypical in the series of maximum annual flows. Univariate mixed probability distribution functions have been developed based on the theory of extreme values, which require techniques to determine their parameters. Therefore, this paper explores a function that considers three populations to analyze maximum annual flows. According to the structure of the Generalized Extreme-Value Distribution (GEV), the simultaneous definition of nine parameters is required: three of location, three of scale, and three of probability of occurrence. Thus, the use of a meta-heuristic technique was proposed (harmonic search). The precision of the adjustment was increased through the optimization of the parameters, and with it came a reduction in the uncertainty of the forecast, particularly for cyclonic events. It is concluded that the use of an extreme value distribution (Type I) structured with three populations and accompanied by the technique of harmonic search improves the performance in respect to classic techniques for the determination of its parameters.

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.

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