• 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.99-106
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• 2008

In this paper, we establish some recurrence relations which is satisfied by the quotient moments of the lower record values from the standard generalized extreme value (GEV) distribution.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.523-529
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• 2010

In this paper, we obtain some recurrence relations for the quotient moments of the lower record values from the generalized extereme value(GEV) distribution. We also deduce some recurrence relations for the negative moments from the GEV distribution.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3B
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• pp.259-267
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• 2009

Generalized Extreme Value (GEV) distribution is recommended for flood frequency and extreme rainfall distribution in many country. L-moment method is the most common estimation procedure for the GEV distribution. In this study, the relationships between the cross-site correlations between extreme events and the cross-correlation of estimators of L-moment ratios (L-moment Coefficient of Variation (L-CV) and L-moment Coefficient of Skewness (L-CS)) for data generated from GEV distribution were derived by Monte Carlo simulation. Those relationships were fit to the simple power function. In this Monte Carlo simulation, GEV+ distribution were employed wherein unrealistic negative values were excluded. The simple power models provide accurate description of the relationships between cross-correlation of data and cross-correlation of L-moment ratios. Estimated parameters and accuracies of the power functions were reported for different GEV distribution parameters combinations. Moreover, this study provided a description about regional regression approach using Generalized Least Square (GLS) regression method which require the cross-site correlation among L-moment estimators. The relationships derived in this study allow regional GLS regression analyses of both L-CV and L-CS estimators that correctly incorporate the cross-correlation among GEV L-moment estimators.

• Journal of Korean Society of Water and Wastewater
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• v.26 no.2
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• pp.321-329
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• 2012

In this study, statistical analysis under both stationary and non-stationary climate was conducted for rainfall data measured in Seoul. Generalised Extreme Value (GEV) distribution and Gumbel distribution were used for the analysis. Rainfall changes under the non-stationary climate were estimated by applying time variable (t) to location parameter (${\xi}$). Rainfall depths calculated in non-stationary climate increased by 1.1 to 6.2mm and 1.0 to 4.6mm for the GEV distribution and gumbel distribution respectively from those stationary forms. Changes in annual maximum rainfall were estimated with rate of change in the location parameter (${\xi}1{\cdot}t$), and temporal changes of return period were predicted. This was also available for re-evaluating the current sewer design return period. Design criteria of sewer system was newly suggested considering life expectance of the system as well as temporal changes in the return period.

• 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.

• Korean Management Science Review
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• v.24 no.2
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• pp.115-126
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• 2007

Weekly minima of daily log returns of Korean composite stock price index 200 and its five industry-based business divisions over the period from January 1990 to December 2005 are fitted using two block-based extreme distributions: Generalized Extreme Value(GEV) and Generalized Logistic(GLO). Parameters are estimated using the probability weighted moments. Applicability of two distributions is investigated using the Monte Carlo simulation based empirical p-values of Anderson Darling test. Our empirical results indicate that both the GLO and GEV models seem to be comparably applicable to the weekly minima. These findings are against the evidences in Gettinby et al.[7], who claimed that the GEV model was not valid in many cases, and supported the significant superiority of the GLO model.

• Journal of Korean Society of Water and Wastewater
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• v.30 no.1
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• pp.41-49
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• 2016

In this study, rainfall characteristics with stationary and non-stationary perspectives were analyzed using generalized extreme value (GEV) distribution and Gumbel distribution models with rainfall data collected in major cities of Korea to reevaluate the return period of sewer flooding in those cities. As a result, the probable rainfall for GEV and Gumbel distribution in non-stationary state both increased with time(t), compared to the stationary probable rainfall. Considering the reliability of ${\xi}_1$, a variable reflecting the increase of storm events due to climate change, the reliability of the rainfall duration for Seoul, Daegu, and Gwangju in the GEV distribution was over 90%, indicating that the probability of rainfall increase was high. As for the Gumbel distribution, Wonju, Daegu, and Gwangju showed the higher reliability while Daejeon showed the lower reliability than the other cities. In addition, application of the maximum annual rainfall change rate (${\xi}_1{\cdot}t$) to the location parameter made possible the prediction of return period by time, therefore leading to the evaluation of design recurrence interval.