• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.249-273
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• 1996

This paper reviews and develops several statistical models for extreme values, based on threshold methodology. Extreme values of a time series are modeled in terms of tails which are defined as truncated forms of original variables, and Markov property is imposed on the tails. Tails of the generalized extreme value distribution and a multivariate extreme value distributively, of the tails of the series. These models are then applied to real ozone data series collected in the Chicago area. A major concern is given to detecting any possible trend in the extreme values.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.537-537
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• 2015

In recent decades, the independence and identical distribution (iid) assumption for extreme events has been shown to be invalid in many cases because long-term climate variability resulting from phenomena such as the Pacific decadal variability and El Nino-Southern Oscillation may induce varying meteorological systems such as persistent wet years and dry years. Therefore, in the current study we propose a new parameter estimation method for probability distribution models to more accurately predict the magnitude of future extreme events when the iid assumption of probability distributions for large-scale climate variability is not adequate. The proposed parameter estimation is based on a metaheuristic approach and is derived from the objective function of the rth power probability-weighted sum of observations in increasing order. The combination of two distributions, gamma and generalized extreme value (GEV), was fitted to the GEV distribution in a simulation study. In addition, a case study examining the annual hourly maximum precipitation of all stations in South Korea was performed to evaluate the performance of the proposed approach. The results of the simulation study and case study indicate that the proposed metaheuristic parameter estimation method is an effective alternative for accurately selecting the rth power when the iid assumption of extreme hydrometeorological events is not valid for large-scale climate variability. The maximum likelihood estimate is more accurate with a low mixing probability, and the probability-weighted moment method is a moderately effective option.

• 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.

• Structural Engineering and Mechanics
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• v.74 no.1
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• pp.55-67
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• 2020

The common practice to predict the characteristic structural load effects (LEs) in long reference periods is to employ the extreme value theory (EVT) for building limit distributions. However, most applications ignore that LEs are driven by multiple loading events and thus do not have the identical distribution, a prerequisite for EVT. In this study, we propose the composite extreme value modeling approach using clustering to (a) cluster initial blended samples into finite identical distributed subsamples using the finite mixture model, expectation-maximization algorithm, and the Akaike information criterion; (b) combine limit distributions of subsamples into a composite prediction equation using the generalized Pareto distribution based on a joint threshold. The proposed approach was validated both through numerical examples with known solutions and engineering applications of bridge traffic LEs on a long-span bridge. The results indicate that a joint threshold largely benefits the composite extreme value modeling, many appropriate tail approaching models can be used, and the equation form is simply the sum of the weighted models. In numerical examples, the proposed approach using clustering generated accurate extrema prediction of any reference period compared with the known solutions, whereas the common practice of employing EVT without clustering on the mixture data showed large deviations. Real-world bridge traffic LEs are driven by multi-events and present multipeak distributions, and the proposed approach is more capable of capturing the tendency of tailed LEs than the conventional approach. The proposed approach is expected to have wide applications to general problems such as samples that are driven by multiple events and that do not have the identical distribution.

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1549-1566
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• 2016

Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.

• Journal of Korea Water Resources Association
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• v.50 no.3
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• pp.211-221
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• 2017

In statistical hydrology, various extreme distributions such as the generalized extreme value (GEV), generalized logistic (GLO) and Gumbel (GUM) models have been widely used to analyze the extreme events. In the case of rainfall events in South Korea, the GEV and Gumbel distributions are known to be appropriate among various extreme distribution models. However, the proper probability distribution model may be different depending on the type of extreme events, rainfall duration, region, and statistical characteristics of extreme events. In this regard, it is necessary to apply a wide range of statistical properties that can be represented by the distribution model because it has two shape parameters. In this study, the statistical applicability of rainfall data is analyzed using the Burr XII distribution and the dimensionless L-moment ratio for 620 stations in South Korea. For this purpose, L-skewness and L-kurtosis of the Burr XII distribution are derived and L-moment ratio diagram is drawn and then the applicability of 620 stations was analyzed. As a result, it is found that the Burr XII distribution for the stations of the Han River basin in which L-skewness is relatively larger than L-kurtosis is appropriate, It is possibility of replacing the distribution of commonly used Gumbel or GEV distributions. Therefore, the Burr XII model can be replaced as an appropriate probability model in this basin.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.3
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• pp.31-42
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• 2004

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 at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• 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.

• 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.

• Journal of the Korean Statistical Society
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• v.28 no.1
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• pp.57-72
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• 1999

Falk(1994) showed that the asymptotic efficiency of the Pickands estimator of the extreme value index $\beta$ can considerably be improved by a simple convex combination. In this paper we propose an alternative estimator of $\beta$ which is as asymptotically efficient as the optimal convex combination of the Pickands estimators but has a better finite-sample performance. We prove consistency and asymptotic normality of the proposed estimator. Monte Carlo simulations are conducted to compare the finite-sample performances of the proposed estimator and the optimal convex combination estimator.