The analysis of PM10 concentrations using the generalized extreme value (GEV) and generalized pareto distribution (GPD) in the Bayesian approach

2018 ◽  
Author(s):  
Hasfazilah Ahmat ◽  
Ahmad Shukri Yahaya
Keyword(s):  
Bayesian Approach ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Extreme Value ◽  
Generalized Extreme Value ◽  
Generalized Pareto ◽  
The Bayesian Approach

scholarly journals Sebaran Generalized Extreme Value (GEV) Dan Generalized Pareto (GP) untuk Pendugaan Curah Hujan Ekstrim di Wilayah DKI Jakarta

2016 ◽  
Vol 7 (1) ◽  
pp. 75-84
Author(s):  
Achi Rinaldi
Keyword(s):  
Pareto Distribution ◽  
Extreme Event ◽  
Generalized Pareto Distribution ◽  
Extreme Value Distribution ◽  
Location Parameter ◽  
Extreme Rainfall ◽  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
Generalized Extreme Value ◽  
Generalized Pareto

Extreme event such as extreme rainfall have been analyzed and most concern for the country all around the world. There are two common distribution for extreme value which are Generalized Extreme Value distribution and Generalized Pareto distribution. These two distribution have shown good performace to estimate the parameter of  extreme value. This research was aim to estimate parameter of extreme value using GEV distribution and GP distribution, and also to characterized effect of extreme event such as flood. The rainfall data was taken from BMKG for 5 location in DKI Jakarta. Both of distribution shown a good perfromance. The resut showed that Tanjung Priok station has biggest location parameter for GEV and also the biggest scale parameter for GP, that mean the biggest probability to take flood effect of the extreme rainfall.

scholarly journals VARIABILIDADE DA ESTIMATIVA DE EVENTOS EXTREMOS DE PRECIPITAÇÃO NO MUNICÍPIO DE MACAÉ – RJ

2021 ◽  
Vol 6 (2) ◽  
Author(s):  
Isabor Viana Sant'Ana Mendes ◽  
Aline Míriam Marques ◽  
Danilo De Assis Amaral ◽  
Bruno Luis da Silva Maia ◽  
Flávia Ribeiro Villela Fernandes ◽  
...  
Keyword(s):  
Analysis Of Variance ◽  
Rio De Janeiro ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Extreme Value ◽  
Generalized Extreme Value ◽  
Generalized Pareto ◽  
Significant Difference ◽  
Post Hoc

O estudo de eventos extremos de precipitação torna-se essencial e relevante devido aos impactos e implicações que estes eventos provocam na sociedade. No município de Macaé esses eventos adversos são constantes, sendo o que mais registrou ocorrência de alagamentos caracterizados como desastres no estado do Rio de Janeiro, no período de 1991 a 2012, no Atlas Brasileiro de Desastres Naturais. Assim, o objetivo deste trabalho foi analisar a variabilidade dos valores obtidos através dos métodos Generalized Extreme Value (GEV) e Generalized Pareto Distribution(GPD) para determinação do nível de retorno de eventos extremos de precipitação no município de Macaé. O modelo estatístico Analysis of Variance (ANOVA) foi adotado e o diagnóstico do modelo validado. Adicionalmente, a análise post hoc foi realizada através do Tukey Honest Significant Difference. As análises estatísticas foram implementadas no ambiente de software R. De fato, constata-se que existem diferenças significativas entre as estimativas dos níveis de precipitação segundo métodos e estação do ano. Os resultados podem auxiliar análises futuras e corroboram com a escolha do melhor método para entender a variação e o comportamento de eventos com grandes volumes pluviométricos em curta duração de tempo ou enxurradas. Sendo portanto, um estudo relevante para auxiliar no planejamento e na implementação de ações de políticas públicas a serem aplicadas em problemas oriundos de tais eventos.

A generalized Pareto distribution–based extreme value model of thermal gradients in a long-span bridge combining parameter updating

2016 ◽  
Vol 20 (2) ◽  
pp. 202-213 ◽  
Author(s):  
Guang-Dong Zhou ◽  
Ting-Hua Yi ◽  
Bin Chen ◽  
Huan Zhang
Keyword(s):  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Extreme Value ◽  
Thermal Gradients ◽  
Long Span Bridges ◽  
Long Span ◽  
Generalized Pareto ◽  
Long Span Bridge ◽  
Extreme Value Model ◽  
Value Model

Estimating extreme value models with high reliability for thermal gradients is a significant task that must be completed before reasonable thermal loads and possible thermal stress in long-span bridges are evaluated. In this article, a generalized Pareto distribution–based extreme value model combining parameter updating has been developed to describe the statistical characteristics of thermal gradients in a long-span bridge. The procedure of excluding correlation and the approach of selecting a proper threshold are suggested to prepare samples for generalized Pareto distribution estimation. A Bayesian estimation, which has the capability of updating model parameters by fusing prior information and incoming monitoring data, is proposed to fit the generalized Pareto distribution–based model. Furthermore, the Gibbs sampling, which is a Markov chain Monte Carlo algorithm, is adopted to derive the Bayesian posterior distribution. Finally, the proposed method is applied to the field monitoring data of thermal gradients in the Jiubao Bridge. The extreme value models of thermal gradients for the Jiubao Bridge are established, and the extreme thermal gradients with different return periods are extrapolated. The results indicate that the generalized Pareto distribution–based extreme value model has a strong ability to represent the statistical features of thermal gradients for the Jiubao Bridge, and the Bayesian estimation combining parameter updating provides high-precision generalized Pareto distribution–based models for predicting extreme thermal gradients. The predicted extreme thermal gradients are expected to evaluate and design long-span bridges.

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 On Compound Distributions for Natural Disaster Modelling in Kenya

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Antony Rono ◽  
Carolyne Ogutu ◽  
Patrick Weke
Keyword(s):  
Natural Disasters ◽  
Pareto Distribution ◽  
Negative Binomial ◽  
Threshold Model ◽  
Generalized Pareto Distribution ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Generalized Pareto ◽  
Compound Distribution ◽  
Poor Infrastructure

Kenyan communities are exposed to natural disasters by an amalgamation of factors such as poverty, aridity, and settlements in areas susceptible to natural disasters or in areas with poor infrastructure. This is expected to increase due to the effects of climate change. In an attempt to explain some of these variabilities, we model the extreme damages from natural disasters in Kenya by developing a compound distribution that takes into account both the frequency and the severity of the extreme events. The resulting distribution is based on a threshold model and compound extreme value distribution. For frequency of events exceeding a threshold of 150,000, we found that it follows a negative binomial distribution, while severity of exceedance follows a generalized Pareto distribution. This distribution fits the data well and is found to be a better model for natural disasters in Kenya than the traditional extreme value threshold model.

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