• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.304-304
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• 2018

이변량 빈도해석은 일반적으로 고정지속기간 강우량에 대해 빈도해석하는 단변량 빈도해석에 비해 지속기간을 확률변수로 이용하여 강우량과 동시에 확률변수로 사용할 수 있다는 장점이 있다. 하지만 확률분포형의 차원이 증가하기 때문에 기존 단변량 빈도해석에서 요구되던 표본크기보다 더 많은 표본이 필요하다. 우리나라 강우관측소의 경우 오래된 관측소의 경우에도 기록년수가 60년을 넘지 않아 연최대계열로 확률표본을 작성할 경우 이변량 빈도해석을 수행하기에 부족할 수 있다. 따라서 본 연구에서는 Peaks Over Threshold (POT) 방법을 이용하여 적정 확률표본을 선택하는 연구를 진행하였다. 서울 기상청 지점의 강우자료로부터 최소무강우시간을 이용하여 모든 강우사상을 추출하였으며 각 강우사상의 강우량과 지속기간이 확률변수로 사용되었다. 기존에 알려진 POT 방법들과 Anderson-Darling 적합도 검정을 이용한 절단값 산정방법등을 적용하여 확률표본 개수의 변화에 따른 주변분포형의 적합도 검정과 이변량 확률모형의 적합성을 살펴보았다.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.101-114
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• 2012

In car insurance, the loss ratio is the ratio of total losses paid out in claims divided by the total earned premiums. In order to minimize the loss to the insurance company, estimating extreme quantiles of loss ratio distribution is necessary because the loss ratio has essential prot and loss information. Like other types of insurance related datasets, the distribution of the loss ratio has heavy-tailed distribution. The Peaks over Threshold(POT) and the Hill estimator are commonly used to estimate extreme quantiles for heavy-tailed distribution. This article compares and analyzes the performances of various kinds of parameter estimating methods by using a simulation and the real loss ratio of car insurance data. In addition, we estimate extreme quantiles using the Hill estimator. As a result, the simulation and the loss ratio data applications demonstrate that the POT method estimates quantiles more accurately than the Hill estimation method in most cases. Moreover, MLE, Zhang, NLS-2 methods show the best performances among the methods of the GPD parameters estimation.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.483-494
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• 2013

The importance of financial risk management has been highlighted after several recent incidences of global financial crisis. One of the issues in financial risk management is how to measure the risk; currently, the most widely used risk measure is the Value at Risk(VaR). We can consider to estimate VaR using extreme value theory if the financial data have heavy tails as the recent market trend. In this paper, we study estimations of VaR using Peaks over Threshold(POT), which is a common method of modeling fat-tailed data using extreme value theory. To use POT, we first estimate parameters of the Generalized Pareto Distribution(GPD). Here, we compare three different methods of estimating parameters of GPD by comparing the performance of the estimated VaR based on KOSPI 5 minute-data. In addition, we simulate data from normal inverse Gaussian distributions and examine two parameter estimation methods of GPD. We find that the recent methods of parameter estimation of GPD work better than the maximum likelihood estimation when the kurtosis of the return distribution of KOSPI is very high and the simulation experiment shows similar results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.3
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• pp.139-154
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• 1993

The major purpose of this study is to develop a regionalized regression model, which predicts flood peaks from the characteristics of the ungaged catchments, through the regional flood frequency analysis for the selected stage gauging stations located on several natural rivers of Korea. The magnitude and the frequency of flood peaks with specified recurrence intervals were estimated from the flood frequency analysis on the 28 selected stage gauging stations distributed on the five major rivers of Korea. The results of the analysis were compared with the predictions from the two different flood frequency models. From the statistical evaluation of these models, it was revealed that the POT model (Peaks Over a Threshold model), which is based on the partial duration method, is more effective in predicting flood peaks from short period records than the ANNMAX model (ANNual MAXimum model) which is based on the annual maximum series method. A regionalized regression model was developed to facilitate the estimation of design floods for ungaged catchments through the regression analysis between flood peaks and the topographic characteristics of the catchments assumed to be important in runoff processes. In addition to this, the correlation diagrams are presented which show the relationships between flood peaks with specified recurrence intervals and the major characteristics of the catchments.

• Ocean Systems Engineering
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• v.4 no.4
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• pp.293-308
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• 2014

Unlike the traditional displacement type vessels, the high speed planing crafts are supported by the lift forces which are highly non-linear. This non-linear phenomenon causes their motions in an irregular seaway to be non-Gaussian. In general, it may not be possible to express the probability distribution of such processes by an analytical formula. Also the process might not be stationary or ergodic in which case the statistical behavior of the motion to be constantly changing with time. Therefore the extreme values of such a process can no longer be calculated using the analytical formulae applicable to Gaussian processes. Since closed form analytical solutions do not exist, recourse is taken to fitting a distribution to the data and estimating the statistical properties of the process from this fitted probability distribution. The peaks over threshold analysis and fitting of the Generalized Pareto Distribution are explored in this paper as an alternative to Weibull, Generalized Gamma and Rayleigh distributions in predicting the short term extreme value of a random process.

• Structural Engineering and Mechanics
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• v.85 no.4
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• pp.531-543
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• 2023

The existing concrete bridges are time-varying working systems, where the maintenance strategy should be planned according to the time-varying performance of the bridge. This work proposes a time-dependent residual capacity assessment procedure, which considers the non-stationary bridge load effects under growing traffic and non-stationary structural deterioration owing to material degradations. Lifetime bridge load effects under traffic growth are predicated by the non-stationary peaks-over-threshold (POT) method using time-dependent generalized Pareto distribution (GPD) models. The non-stationary structural resistance owing to material degradation is modeled by incorporating the Gamma deterioration process and field inspection data. A three-span continuous box-girder bridge is illustrated as an example to demonstrate the application of the proposed procedure, and the time-varying reliability indexes of the bridge girder are calculated. The accuracy of the proposed non-stationary POT method is verified through numerical examples, where the shape parameter of the time-varying GPD model is constant but the threshold and scale parameters are polynomial functions increasing with time. The case study illustrates that the residual flexural capacities show a degradation trend from a slow decrease to an accelerated decrease under traffic growth and material degradation. The reliability index for the mid-span cross-section reduces from 4.91 to 4.55 after being in service for 100 years, and the value is from 4.96 to 4.75 for the mid-support cross-section. The studied bridge shows no safety risk under traffic growth and structural deterioration owing to its high design safety reserve. However, applying the proposed numerical approach to analyze the degradation of residual bearing capacity for bridge structures with low safety reserves is of great significance for management and maintenance.

• 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.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.717-732
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• 2011

We consider bootstrap confidence intervals for high quantiles of heavy-tailed distribution. A semi-parametric method is compared with the non-parametric and the parametric method through simulation study.

• Journal of Korea Water Resources Association
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• v.43 no.8
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• pp.733-745
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• 2010

Seasonality of hydrologic extreme variable is a significant element from a water resources managemental point of view. It is closely related with various fields such as dam operation, flood control, irrigation water management, and so on. Hydrological frequency analysis conjunction with partial duration series rather than block maxima, offers benefits that include data expansion, analysis of seasonality and occurrence. In this study, nonstationary frequency analysis based on the Bayesian model has been suggested which effectively linked with advantage of POT (peaks over threshold) analysis that contains seasonality information. A selected threshold that the value of upper 98% among the 24 hours duration rainfall was applied to extract POT series at Seoul station, and goodness-fit-test of selected GEV distribution has been examined through graphical representation. Seasonal variation of location and scale parameter ($\mu$ and $\sigma$) of GEV distribution were represented by Fourier series, and the posterior distributions were estimated by Bayesian Markov Chain Monte Carlo simulation. The design rainfall estimated by GEV quantile function and derived posterior distribution for the Fourier coefficients, were illustrated with a wide range of return periods. The nonstationary frequency analysis considering seasonality can reasonably reproduce underlying extreme distribution and simultaneously provide a full annual cycle of the design rainfall as well.

• Journal of Korea Water Resources Association
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• v.45 no.3
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• pp.275-290
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• 2012

In this study, we have developed an optimal time distribution model through extraction of peaks over threshold (POT) series. The median values for annual maximum rainfall dataset, which are obtained from the magnetic recording (MMR) and the automatic weather system(AWS) data at Seoul meteorological observatory, were used as the POT criteria. We also suggested the improved methodology for the time distribution of extreme rainfall compared to Huff method, which is widely used for time distributions of design rainfall. The Huff method did not consider changing in the shape of time distribution for each rainfall durations and rainfall criteria as total amount of rainfall for each rainfall events. This study have suggested an extracting methodology for rainfall events in each quartile based on interquartile range (IQR) matrix and selection for the mode quartile storm to determine the ranking cosidering weighting factors on minutely observation data. Finally, the optimal time distribution model in each rainfall duration was derived considering both data size and characteristics of distribution using kernel density function in extracted dimensionless unit rainfall hyetograph.