scholarly journals Parameter estimation and threshold selection uncertainty in extreme wind speed distribution – A frequentist approach with generalized Pareto distribution using automatic threshold selection

Időjárás ◽  
2020 ◽  
Vol 124 (3) ◽  
pp. 311-330
Author(s):  
Ágnes Kenéz ◽  
Attila László Joó
Keyword(s):  
Parameter Estimation ◽  
Wind Speed ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Threshold Selection ◽  
Speed Distribution ◽  
Generalized Pareto ◽  
Wind Speed Distribution ◽  
Extreme Wind ◽  
Extreme Wind Speed

scholarly journals Extreme wind speed distribution in a mixed wind climate

2018 ◽  
Vol 176 ◽  
pp. 239-253 ◽  
Author(s):  
Shi Zhang ◽  
Giovanni Solari ◽  
Qingshan Yang ◽  
Maria Pia Repetto
Keyword(s):  
Wind Speed ◽  
Speed Distribution ◽  
Wind Speed Distribution ◽  
Extreme Wind ◽  
Extreme Wind Speed ◽  
Wind Climate

scholarly journals A New Parameter Estimator for the Generalized Pareto Distribution under the Peaks over Threshold Framework

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 406 ◽  
Author(s):  
Xu Zhao ◽  
Zhongxian Zhang ◽  
Weihu Cheng ◽  
Pengyue Zhang
Keyword(s):  
Value At Risk ◽  
Environmental Science ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
High Threshold ◽  
Threshold Selection ◽  
Peaks Over Threshold ◽  
Scale Parameters ◽  
Generalized Pareto ◽  
Critical Issues

Techniques used to analyze exceedances over a high threshold are in great demand for research in economics, environmental science, and other fields. The generalized Pareto distribution (GPD) has been widely used to fit observations exceeding the tail threshold in the peaks over threshold (POT) framework. Parameter estimation and threshold selection are two critical issues for threshold-based GPD inference. In this work, we propose a new GPD-based estimation approach by combining the method of moments and likelihood moment techniques based on the least squares concept, in which the shape and scale parameters of the GPD can be simultaneously estimated. To analyze extreme data, the proposed approach estimates the parameters by minimizing the sum of squared deviations between the theoretical GPD function and its expectation. Additionally, we introduce a recently developed stopping rule to choose the suitable threshold above which the GPD asymptotically fits the exceedances. Simulation studies show that the proposed approach performs better or similar to existing approaches, in terms of bias and the mean square error, in estimating the shape parameter. In addition, the performance of three threshold selection procedures is assessed by estimating the value-at-risk (VaR) of the GPD. Finally, we illustrate the utilization of the proposed method by analyzing air pollution data. In this analysis, we also provide a detailed guide regarding threshold selection.

Application of differential evolution for wind speed distribution parameters estimation

2021 ◽  
pp. 0309524X2199996
Author(s):  
Rajesh Kumar ◽  
Arun Kumar
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Wind Speed ◽  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Speed Distribution ◽  
De Algorithm ◽  
Wind Speed Distribution ◽  
Distribution Parameters

Weibull distribution is an extensively used statistical distribution for analyzing wind speed and determining energy potential studies. Estimation of the wind speed distribution parameter is essential as it significantly affects the success of Weibull distribution application to wind energy. Various estimation methods viz. graphical method, moment method (MM), maximum likelihood method (ML), modified maximum likelihood method, and energy pattern factor method or power density method have been presented in various reported research studies for accurate estimation of distribution parameters. ML is the most preferred approach to study the parameter estimation. ML works on the principle of forming a likelihood function and maximizing the function for parameter estimation. ML generally uses the numerical based iterative method, such as Newton–Raphson. However, the iterative methods proposed in the literature are generally computationally intensive. In this paper, an efficient technique utilizing differential evolution (DE) algorithm to enhance the estimation accuracy of maximum likelihood estimation has been presented. The [Formula: see text] of GA-Weibull, SA-Weibull, and DE-Weibull is 0.958, 0.953, and 0.973 respectively, and value of RMSE of DE-Weibull 0.0083, GA-Weibull (0.0104), and SA-Weibull (0.0110), for the yearly wind speed data are obtained. The lowest root mean square error and larger regression value for both monthly and yearly wind speed data indicate that the DE-Weibull distribution has the best goodness of fit and advocate the DE algorithm for the parameter estimation.

scholarly journals ON THE TWO STEP THRESHOLD SELECTION FOR OVER-THRESHOLD MODELLING

2012 ◽  
Vol 1 (33) ◽  
pp. 42
Author(s):  
Pietro Bernardara ◽  
Franck Mazas ◽  
Jérôme Weiss ◽  
Marc Andreewsky ◽  
Xavier Kergadallan ◽  
...  
Keyword(s):  
Pareto Distribution ◽  
Extreme Values ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Water Levels ◽  
Distributed Data ◽  
Threshold Selection ◽  
The Past ◽  
Generalized Pareto ◽  
Selection For

In the general framework of over-threshold modelling (OTM) for estimating extreme values of met-ocean variables, such as waves, surges or water levels, the threshold selection logically requires two steps: the physical declustering of time series of the variable in order to obtain samples of independent and identically distributed data then the application of the extreme value theory, which predicts the convergence of the upper part of the sample toward the Generalized Pareto Distribution. These two steps were often merged and confused in the past. A clear framework for distinguishing them is presented here. A review of the methods available in literature to carry out these two steps is given here together with the illustration of two simple and practical examples.

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