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.

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 Statistical modelling of extreme rainfall in Peninsular Malaysia

2021 ◽  
Vol 36 ◽  
pp. 01012
Author(s):  
Wei Lun Tan ◽  
Woon Shean Liew ◽  
Lloyd Ling
Keyword(s):  
Predictive Analytics ◽  
Extreme Value Distribution ◽  
Extreme Rainfall ◽  
Statistical Modelling ◽  
Flash Floods ◽  
Extreme Value ◽  
Peninsular Malaysia ◽  
Generalized Extreme Value Distribution ◽  
Generalized Extreme Value ◽  
Rainfall Model

Flash floods are known as one of the common natural disasters that cost over billions of Ringgit Malaysia throughout history. Academically, an extreme rainfall model is effective in modelling to predict and prevent the occurrence of flash floods. This paper compares four probability distributions, namely, exponential distribution, generalized extreme value distribution, gamma distribution, and Weibull distribution, with the rainfall data of 10 stations in peninsular Malaysia. The period of the data is from 1975 to 2008. The comparison is based on the descriptive and predictive analytics of the models. The determination of the most effective model is through Kolmogorov-Smirnov, Anderson-Darling, and chi-square test. The result shows that generalized extreme value is the most preferred extreme rainfall model for the rainfall cases in Peninsular Malaysia.

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.

scholarly journals Extreme Value Distributions on Closing Quotations and Returns of Islamabad Stock Exchange

2019 ◽  
pp. 1-9
Author(s):  
Muhammad Anas ◽  
Nasir Jamal ◽  
Muhammad Hanif ◽  
Usman Shahzad
Keyword(s):  
Banking Sector ◽  
Stock Exchange ◽  
Generalized Pareto Distribution ◽  
Secondary Data ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
R Language ◽  
Generalized Pareto ◽  
Best Fit

This study is an experimental test done on the secondary data of banking sector of Islamabad Stock Exchange for year 2017 and applied different techniques on the given data record by using Generalized Extreme Value Distribution (GEV), Gumble Distribution (GBL), Generalized Pareto Distribution (GPD), Exponential Distribution (EXP), Gamma Distribution (GAM), Weibull Distribution (WBL) on the data of four banks Habib Bank, Allied Bank, Bank Alfalah and Askari Bank. This data is concerning the closing quotations and returns of four banks registered in Islamabad Stock Exchange. We try to fit different distributions on the data and founnd the best fit distribution. We estimated the parameters of each distribution and also find the standard deviations of each distribution by using R Language and find which distribution is the best fit distribution on the basis of standard deviation distribution. We analyzed that shape wise GEV is the most suitable distribution, scale wise EXP distribution the best and location wise the best one is Gumbal distribution. This article shows that the overall GEV is the best distribution to model correctly the data.

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.

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