• Journal of Korea Water Resources Association
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• v.48 no.5
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• pp.331-343
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• 2015

Most nonstationary frequency models are defined as the probability models containing the time-dependent parameters. For frequency analysis of annual maximum rainfall data, the Gumbel distribution is generally recommended in Korea. For the nonstationary Gumbel models, the time-dependent location and scale parameters are defined as linear and exponential relationship, respectively. The exponentially time-varying scale parameter of nonstationary Gumbel model is generally used because the scale parameter should be positive. However, the exponential form of scale parameter occasionally provides overestimated quantiles. In this study, various forms of time-varying scale parameters such as exponential, linear, and logarithmic forms were proposed and compared. The parameters were estimated based on the method of maximum likelihood. To compare the accuracy of each scale parameter, Monte Carlo simulation was performed for various conditions. Additionally, nonstationary frequency analysis was conducted for the sites which have more than 30 years data with a trend in rainfall data. As a result, nonstationary Gumbel model with exponentially time-varying scale parameter generally has the smallest root mean square error comparing with another forms.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.145-153
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• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.

• Journal of Korea Water Resources Association
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• v.49 no.5
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• pp.411-422
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• 2016

Rainfall-runoff modeling in conjunction with rainfall frequency analysis has been widely used for estimating design floods in South Korea. However, uncertainties associated with underlying distribution and sampling error have not been properly addressed. This study applied a Bayesian method to quantify the uncertainties in the rainfall frequency analysis along with Gumbel distribution. For a purpose of comparison, a probability weighted moment (PWM) was employed to estimate confidence interval. The uncertainties associated with design rainfalls were quantitatively assessed using both Bayesian and PWM methods. The results showed that the uncertainty ranges with PWM are larger than those with Bayesian approach. In addition, the Bayesian approach was able to effectively represent asymmetric feature of underlying distribution; whereas the PWM resulted in symmetric confidence interval due to the normal approximation. The use of long period data provided better results leading to the reduction of uncertainty in both methods, and the Bayesian approach showed better performance in terms of the reduction of the uncertainty.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.453-462
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• 2009

Studies on software plagiarism detection, prevention and judgement have become widespread due to the growing of interest and importance for the protection and authentication of software intellectual property. Many previous studies focused on comparing all pairs of submitted codes by using attribute counting, token pattern, program parse tree, and similarity measuring algorithm. It is important to provide a clear-cut model for distinguishing plagiarism and collaboration. This paper proposes a source code clustering algorithm using a probability model on extreme value distribution. First, we propose an asymmetric distance measure pdist($P_a$, $P_b$) to measure the similarity of $P_a$ and $P_b$ Then, we construct the Plagiarism Direction Graph (PDG) for a given program set using pdist($P_a$, $P_b$) as edge weights. And, we transform the PDG into a Gumbel Distance Graph (GDG) model, since we found that the pdist($P_a$, $P_b$) score distribution is similar to a well-known Gumbel distribution. Second, we newly define pseudo-plagiarism which is a sort of virtual plagiarism forced by a very strong functional requirement in the specification. We conducted experiments with 18 groups of programs (more than 700 source codes) collected from the ICPC (International Collegiate Programming Contest) and KOI (Korean Olympiad for Informatics) programming contests. The experiments showed that most plagiarized codes could be detected with high sensitivity and that our algorithm successfully separated real plagiarism from pseudo plagiarism.

• Journal of Industrial Technology
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• v.35
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• pp.95-102
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• 2015

Two extreme wind speed prediction models, the EWM(Extreme wind speed model) in IEC61400-1 and the Gumbel method were compared in this study. The two models were used to predict extreme wind speeds of six different sites in Korea and the results were compared with long term wind data. The NCAR reanalysis data were used for inputs to two models. Various periods of input wind data were tried from 1 year to 50 years and the results were compared with the 50 year maximum wind speed of NCAR wind data. It was found that the EWM model underpredicted the extreme wind speed more than 5 % for two sites. Predictions from Gumbel method overpredicted the extreme wind speed or underpredicted it less than 5 % for all cases when the period of the input data is longer than 10 years. The period of the input wind data less than 3 years resulted in large prediction errors for Gumbel method. Predictions from the EWM model were not, however, much affected by the period of the input wind data.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.41-41
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• 2016

최근 다변량 확률모형을 이용한 빈도해석이 수문자료 등에 적용되면서 다양하게 연구되고 있으며 다변량 확률모형 중 copula 모형은 주변분포형에 대한 제약이 없어 여러 분야에 걸쳐 활발히 연구되고 있다. 강우자료는 기존 일변량 빈도해석을 수행하기 위하여 사용하던 block maxima 방법 대신 최소무강우시간(inter event time)을 통하여 강우사상을 추출하여 표본으로 사용한다. 또한 기후변화로 인한 강우량의 변화등에 대응하기 위하여 비정상성 Generalized Extreme Value(GEV)와 Gumbel 등의 확률분포형에 대한 연구도 많은 부분 이루어져 있다. 본 연구에서는, Archimedean copula 모형을 이용하여 이변량 확률모형을 구축하면서 여기에 사용되는 주변분포형에 정상성/비정상성 분포형을 적용하였다. 모형의 매개변수는 inference function for margin 방법을 이용하였으며 주변분포형으로는 정상성/비정상성 GEV, Gumbel 모형을 적용하였다. 결과로 정상성/비정상성 경향을 나타내는 지점을 구분하고 각 지점에 대한 정상성/비정상성 주변분포형을 적용한 이변량 확률분포형을 구하였다.

• Journal of Korea Water Resources Association
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• v.42 no.9
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• pp.725-736
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• 2009

A flood event can be defined by three characteristics; peak discharge, total flood volume, and flood duration, which are correlated each other. However, a conventional flood frequency analysis for the hydrological plan, design, and operation has focused on evaluating only the amount of peak discharge. The interpretation of this univariate flood frequency analysis has a limitation in describing the complex probability behavior of flood events. This study proposed a bivariate flood frequency analysis using a Gumbel mixed model for the flood evaluation. A time series of annual flood events was extracted from observations of inflow to the Soyang River Dam and the Daechung Dam, respectively. The joint probability distribution and return period were derived from the relationship between the amount of peak discharge and the total volume of flood runoff. The applicability of the Gumbel mixed model was tested by comparing the return periods acquired from the proposed bivariate analysis and the conventional univariate analysis.

• Journal of Korea Water Resources Association
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• v.52 no.11
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• pp.895-904
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• 2019

It has been well recognized that extreme rainfall process often features a nonstationary behavior, which may not be effectively modeled within a stationary frequency modeling framework. Moreover, extreme rainfall events are often described by a two (or more)-component mixture distribution which can be attributed to the distinct rainfall patterns associated with summer monsoons and tropical cyclones. In this perspective, this study explores a Mixture Distribution based Nonstationary Frequency (MDNF) model in a changing rainfall patterns within a Bayesian framework. Subsequently, the MDNF model can effectively account for the time-varying moments (e.g. location parameter) of the Gumbel distribution in a two (or more)-component mixture distribution. The performance of the MDNF model was evaluated by various statistical measures, compared with frequency model based on both stationary and nonstationary mixture distributions. A comparison of the results highlighted that the MDNF model substantially improved the overall performance, confirming the assumption that the extreme rainfall patterns might have a distinct nonstationarity.

• Journal of Wetlands Research
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• v.2 no.1
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• pp.49-58
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• 2000

The frequency analysis of annual maximum rainfall data and the derivation of probable rainfall intensity formula at Masan station are performed in this study. Based on the eight different rainfall duration data from 10 minutes to 24 hours, eight types of probability distribution (Gamma, Lognormal, Log-Pearson type III, GEV, Gumbel, Log-Gumbel, Weibull, and Wakeby distributions), three types of parameter estimation scheme (moment, maximum likelihood and probability weighted methods) and three types of goodness-of-fit test (${\chi}^2$, Kolmogorov-Smirnov and Cramer von Mises tests) were considered to find an appropriate probability distribution at Masan station. The Lognormal-2 distribution was selected and the probable rainfall intensity formula was derived by regression analysis. The derived formula can be used for estimating rainfall quantiles of the Masan vicinity areas with convenience and reliability in practice.

• KCID journal
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• v.2 no.1
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• pp.20-29
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• 1995

It was attempted to get an optimal method for the prediction of design low flows among derivation . techniques of design low flows. Derivation techniques of design low Hon used in this study are Type III extremal, Gumbel-Chow distribution, SMEMAX(Small, M