• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.793-798
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• 2008

Extreme value inference deals with fitting the generalized extreme value distribution model and the generalized Pareto distribution model, which are recently combined to give a single model, namely a two-dimensional non-homogeneous Poisson exceedance point process model. In this paper, we extend the two-dimensional non-homogeneous Poisson process model to include non-stationary effect or dependence on covariates and then derive the likelihood for the extended model.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.535-545
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• 2015

In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.

• Journal of the Korean Society of Industry Convergence
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• v.8 no.2
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• pp.85-95
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• 2005

The margin level in the futures market platys an important role in balancing the default probability with the investor's opportunity cost. In this paper, we investigate whether the movement of KOSPI200 futures daily prices can be modeled with the extreme value theory. Based on this investigation, we examine the validity of the margin level set by the extreme value theory. Moreover, we propose an expected profit-maximization model for securities companies. In this model, the extreme value theory is used for cost estimation, and a regression analysis is used for revenue calculation. Computational results are presented to compare the extreme value distribution with the empirical distribution of margin violation in KOSPI200 and to examine the suitability of the expected profit-maximization model.

• Ocean and Polar Research
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• v.43 no.1
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• pp.1-14
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• 2021

In this study, extreme wind speeds in the Western North Pacific (WNP) were estimated using reanalysis wind fields synthesized with an empirical typhoon vortex model. Reanalysis wind data used is the Fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5) data, which was deemed to be the most suitable for extreme value analysis in this study. The empirical typhoon vortex model used has the advantage of being able to realistically reproduce the asymmetric winds of a typhoon by using the gale/storm-forced wind radii information in the 4 quadrants of a typhoon. Using a total of 39 years of the synthesized reanalysis wind fields in the WNP, extreme value analysis is applied to the General Pareto Distribution (GPD) model based on the Peak-Over-Threshold (POT) method, which can be used effectively in case of insufficient data. The results showed that the extreme analysis using the synthesized wind data significantly improved the tendency to underestimate the extreme wind speeds compared to using only reanalysis wind data. Considering the difficulty of obtaining long-term observational wind data at sea, the result of the synthesized wind field and extreme value analysis developed in this study can be used as basic data for the design of offshore structures.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.463-477
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• 2009

Parameter estimation methods such as maximum likelihood estimation method, probability weighted moments method, regression method have been popularly applied to various extreme value models in numerous literature. Among three methods above, the performance of regression method has not been rigorously investigated yet. In this paper the regression method is compared with the other methods via Monte Carlo simulation studies for estimation of parameters of the Generalized Extreme Value(GEV) distribution and the Generalized Pareto(GP) distribution. Our simulation results indicate that the regression method tends to outperform other methods under small samples by providing smaller biases and root mean square errors for estimation of location parameter of the GEV model. For the scale parameter estimation of the GP model under small samples, the regression method tends to report smaller biases than the other methods. The regression method tends to be superior to other methods for the shape parameter estimation of the GEV model and GP model when the shape parameter is -0.4 under small and moderately large samples.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.947-958
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• 2014

Understanding extreme precipitation events is very important for flood planning purposes. Especially, the r-year return level is a common measure of extreme events. In this paper, we present a spatial analysis of precipitation return level using hierarchical Bayesian modeling. For intensity, we model annual maximum daily precipitations and daily precipitation above a high threshold at 62 stations in Korea with generalized extreme value(GEV) and generalized Pareto distribution(GPD), respectively. The spatial dependence among return levels is incorporated to the model through a latent Gaussian process of the GEV and GPD model parameters. We apply the proposed model to precipitation data collected at 62 stations in Korea from 1973 to 2011.

• Journal of Ocean Engineering and Technology
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• v.33 no.3
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• pp.222-228
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• 2019

An extreme value analysis (EVA) is essential to obtain a design value for highly nonlinear variables such as long-term environmental data for wind and waves, and slamming or sloshing impact pressures. According to the extreme value theory (EVT), the extreme value distribution is derived by multiplying the initial cumulative distribution functions for independent and identically distributed (IID) random variables. However, in the position mooring of DNVGL, the sampled global maxima of the mooring line tension are assumed to be IID stochastic variables without checking their independence. The ITTC Recommended Procedures and Guidelines for Sloshing Model Tests never deal with the independence of the sampling data. Hence, a design value estimated without the IID check would be under- or over-estimated because of considering observations far away from a Weibull or generalized Pareto distribution (GPD) as outliers. In this study, the IID sampling data are first checked in an EVA. With no IID random variables, an automatic resampling scheme is recommended using the block maxima approach for a generalized extreme value (GEV) distribution and peaks-over-threshold (POT) approach for a GPD. A partial autocorrelation function (PACF) is used to check the IID variables. In this study, only one 5 h sample of sloshing test results was used for a feasibility study of the resampling IID variables approach. Based on this study, the resampling IID variables may reduce the number of outliers, and the statistically more appropriate design value could be achieved with independent samples.

• The Journal of the Convergence on Culture Technology
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• v.8 no.1
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• pp.531-536
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• 2022

This paper compared the performance of the parametric method and the nonparametric method when estimating the distribution for the tail of the distribution with heavy tails. For the parametric method, the generalized extreme value distribution and the generalized Pareto distribution were used, and for the nonparametric method, the kernel density estimation method was applied. For comparison of the two approaches, the results of function estimation by applying the block maximum value model and the threshold excess model using daily fine dust public data for each observatory in Seoul from 2014 to 2018 are shown together. In addition, the area where high concentrations of fine dust will occur was predicted through the return level.

• Journal of Korean Society of Water and Wastewater
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• v.30 no.4
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• pp.369-379
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• 2016

It was confirmed that the extreme value distribution model applies to probability of exceeding more than once a day monthly the facility capacities using data of daily maximum inflow rate for 7 wastewater treatment plant. The result of applying the extreme value model, A, D, E wastewater treatment plant has a problem compared to B, C, F, G wastewater treatment plant. but all the wastewater treatment plant has a problem except C, F wastewater treatment plant based 80% of facility capacity. In conclusion, if you make a standard in statistical aspects probability exceeding more than once a day monthly can be 'exceed day is less than a few times annually' or 'probability of exceeding more than once a day monthly is less than what percent'.

• Wind and Structures
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• v.34 no.6
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• pp.469-482
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• 2022

The generalized extreme value distribution (GEVD) is frequently used to fit the block maximum of environmental parameters such as the annual maximum wind speed. There are several methods for estimating the parameters of the GEV distribution, including the least-squares method (LSM). However, the application of the LSM with the expected order statistics has not been reported. This study fills this gap by proposing a fitting method based on the expected order statistics. The study also proposes a plotting position to approximate the expected order statistics; the proposed plotting position depends on the distribution shape parameter. The use of this approximation for distribution fitting is carried out. Simulation analysis results indicate that the developed fitting procedure based on the expected order statistics or its approximation for GEVD is effective for estimating the distribution parameters and quantiles. The values of the probability plotting correlation coefficient that may be used to test the distributional hypothesis are calculated and presented. The developed fitting method is applied to extreme thunderstorm and non-thunderstorm winds for several major cities in Canada. Also, the implication of using the GEVD and Gumbel distribution to model the extreme wind speed on the structural reliability is presented and elaborated.