• 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.

• 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.

• Atmosphere
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• v.26 no.4
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• pp.697-709
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• 2016

This study estimates and evaluates the extreme value of 30 m-resolution daily maximum and minimum temperatures over South Korea, using inverse distance weighting (IDW), parameter-elevation regression on independent slopes model (PRISM) and generalized extreme value (GEV) method. The three experiments are designed and performed to find the optimal estimation strategy to obtain extreme value. First experiment (EXP1) applies GEV firstly to automated surface observing system (ASOS) to estimate extreme value and then applies IDW to produce high-resolution extreme values. Second experiment (EXP2) is same as EXP1, but using PRISM to make the high-resolution extreme value instead of IDW. Third experiment (EXP3) firstly applies PRISM to ASOS to produce the high-resolution temperature field, and then applies GEV method to make high resolution extreme value data. By comparing these 3 experiments with extreme values obtained from observation data, we find that EXP3 shows the best performance to estimate extreme values of maximum and minimum temperatures, followed by EXP1 and EXP2. It is revealed that EXP1 and EXP2 have a limitation to estimate the extreme value at each grid point correctly because the extreme values of these experiments with 30 m-resolution are calculated from only 60 extreme values obtained from ASOS. On the other hand, the extreme value of EXP3 is similar to observation compared to others, since EXP3 produces 30m-resolution daily temperature through PRISM, and then applies GEV to that result at each grid point. This result indicates that the quality of statistically produced high-resolution extreme values which are estimated from observation data is different depending on the combination and procedure order of statistical methods.

• 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.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2002.10a
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• pp.225-228
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• 2002

This research seeks to derive the design rainfalls through the L-moment with the test of homogeneity, independence and outlier of data on annual maximum daily rainfall in 38 Korean rainfall stations. To select the fit appropriate distribution of annual maximum daily rainfall data according to rainfall stations, applied were Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) probability distributions were applied. and their aptness was judged Dusing an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test, the aptitude was judged of applied distributions such as GEV, GLO and GPA. The GEV and GLO distributions were selected as the appropriate distributions. Their parameters were estimated Targetingfrom the observed and simulated annual maximum daily rainfalls and using Monte Carlo techniques, the parameters of GEV and GLO selected as suitable distributions were estimated and. dDesign rainfallss were then derived, using the L-moment. Appropriate design rainfalls were suggested by doing a comparative analysis of design rainfall from the GEV and GLO distributions according to rainfall stations.

• 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.

• The Korean Journal of Applied Statistics
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• v.28 no.2
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• pp.137-149
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• 2015

Flood planning needs to recognize trends for extreme precipitation events. Especially, the r-year return level is a common measure for extreme events. In this paper, we present a nonstationary temporal model for precipitation return levels using a hierarchical Bayesian modeling. For intensity, we model annual maximum daily precipitation measured in Korea with a generalized extreme value (GEV). The temporal dependence among the return levels is incorporated to the model for GEV model parameters and a linear model with autoregressive error terms. We apply the proposed model to precipitation data collected from various stations in Korea from 1973 to 2011.