• KSCE Journal of Civil and Environmental Engineering Research
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• v.38 no.2
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• pp.249-259
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• 2018

More than half of annual rainfall occurs in summer season in Korea due to its climate condition and geographical location. A frequency analysis is mostly adopted for designing hydraulic structure under the such concentrated rainfall condition. Among the various distributions, univariate Gumbel distribution has been routinely used for rainfall frequency analysis in Korea. However, the distributional changes in extreme rainfall have been globally observed including Korea. More specifically, the univariate Gumbel distribution based rainfall frequency analysis is often fail to describe multimodal behaviors which are mainly influenced by distinct climate conditions during the wet season. In this context, we purposed a Gumbel mixture distribution based rainfall frequency analysis with a Bayesian framework, and further the results were compared to that of the univariate. It was found that the proposed model showed better performance in describing underlying distributions, leading to the lower Bayesian information criterion (BIC) values. The mixed Gumbel distribution was more robust for describing the upper tail of the distribution which playes a crucial role in estimating more reliable estimates of design rainfall uncertainty occurred by peak of upper tail than single Gumbel distribution. Therefore, it can be concluded that the mixed Gumbel distribution is more compatible for extreme frequency analysis rainfall data with two or more peaks on its distribution.

• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.147-152
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• 2003

본 논문에서는 일반화극치분포(GEV)와 r개의 순서통계량을 이용한 r-GEV를 기술하였다. 모수 $\mu,\;\sigma$, k 를 추정하기 위해 최우추정법(MLE)과 Penalized MLE(P-MLE) 방법을 적용해 보았다. 이 분포를 원/달러 환율자료에 적용하여 일종의 재정위기 분석을 실시하였다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.21 no.6
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• pp.480-494
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• 2009

Long term extreme wave data are essential for planning and designing coastal structures. Since the availability of the field data for the waters around Korean peninsula is limited to provide a reliable wave statistics, the wave climate information has been generated by means of long-term wave hindcasting using available meteorological data. KORDI(2005) has proposed extreme wave data at 106 stations off the Korean coast from 1979 to 2003. In this paper, extreme data sets of wave(KORDI, 2005) have been analyzed for best-fitting distribution functions, for which the spread parameter proposed by Goda(2004) is evaluated. The calculated values of the spread parameter are in good agreement with the values based on method of moment for parameter estimation. However, the spread parameter of extreme wave data has a representative value ranging from about 1.0 to 2.8 which is larger than some foreign coastal waters, it is necessary to review deep water design wave.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.20 no.5
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• pp.482-490
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• 2008

For a coastal or harbor structure design, one of the most important environmental factors is the appropriate extreme highest tide level condition. Especially, the information of extreme highest tide level distribution is essential for reliability design. In this paper, 23 set of extreme highest tide level data obtained from National Oceanographic Research Institute(NORI) were analyzed for extreme highest tide levels. The probability distributions considered in this research were Generalized Extreme Value(GEV), Gumbel, and Weibull distribution. For each of these distributions, three parameter estimation methods, i.e. the method of moments, maximum likelihood and probability weighted moments, were applied. Chi-square and Kolmogorov-Smirnov goodness-offit tests were performed, and the assumed distribution was accepted at the confidence level 95%. Gumbel distribution which best fits to the 22 tidal station was selected as the most probable parent distribution, and optimally estimated parameters and extreme highest tide level with various return periods were presented. The extreme values of Incheon, Cheju, Yeosu, Pusan, and Mukho, which estimated by Shim et al.(1992) are lower than that of this result.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.2
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• pp.223-230
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• 2012

The strength of brittle material has commonly been characterized by a normal distribution or Weibull distribution, but it may fit the gamma distribution for some material. The use of an extreme value distribution is proper when the largest values of a set of stresses dominate the failure of the material. This paper presents a formula for reliability estimation based on stress-strength interference theory that is applicable when the strength of material is distributed like a gamma distribution and the stress is distributed like an extreme value distribution. We verified the validity of the equation for the reliability estimation by examining the relationships among the factor of safety, the coefficient of variation, and the reliability. The required minimum factor of safety and the highest allowable coefficient of variation of stress can be estimated by choosing an objective reliability and estimating the reliabilities obtained for various factors of safety and coefficients of variation.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.39-39
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• 2015

극치 수문(Hydrologic extremes)분야에서는 수문자료의 분포에 따라 Gumbel, GEV, 그리고 GLO 분포와 같은 다양한 확률통계 분포형이 존재한다. GEV와 GLO 분포형의 경우 Gumbel 분포형과 달리 형상매개변수가 포함된 3변수 분포형으로써 이상 기후 현상으로 인한 잦은 극치 수문사상을 표현하는데 좀 더 유연한 것으로 알려져 있다. 특히 GLO 분포형의 경우 영국에서 홍수빈도해석 시 적정분포형으로 선정된바 있다(Institute of Hydrology, 1999). 다양한 분포형 중에서 표본 자료를 대표할 수 있는 분포형을 선정하는 통계적 기법이 적합도 검정이다. 적합도 검정에는 $x^2$-검정, Cramer von-Mises 검정, Kolmogorov-Smirnov 검정, PPCC(probability plot correlation coefficient, 확률도시 상관계수)검정 등이 있으며 그 중 PPCC 검정은 이용방법이 간편하면서도 뛰어난 기각능력을 보이는 것으로 알려져 있다. 본 연구에서는 극치 수문분야에서 널리 이용되고 있는 GLO 분포형을 대상으로 자료의 왜곡도 영향을 고려할 수 있는 확률도시 상관계수 검정의 검정통계량을 추정하여 보았다.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.4
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• pp.313-319
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• 2007

Long term wave climate of both extreme and operational wave height is essential for planning and designing coastal structures. Since the availability of the field wave data for the waters around Korean peninsula is limited to provide a reliable wave statistics, the wave climate information has been generated by means of long-term wave hindcasting using available meteorological data. In this paper, a set of deep water wave data obtained from KORDI(2003) were analyzed for extreme wave heights. These wave data at 67 stations off the Korean coast from 1979 to 1998 were arranged in the 16 directions. The probability distributions considered in this research were the FT-I and Weibull distribution. For each of these distributions, the method proposed by Goda(2004) was applied to estimate the parameters. For judgment of best fitting, MIR criterion proposed by Goda and Gobune(1990) was used. FT-I distribution which best fits to the 886 data, while Weibull(k=0.75) 81 data, Weibull(k=1.00) 105 data.

• Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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• 2003.08a
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• pp.359-362
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• 2003

심해 설계파를 추정하는 과정은 일반적으로 극치분포함수에 의한 방법에 의존한다. 극치분포함수를 이용하여 재현기간별 극값을 추출하는 방법은 가용한 자료를 일정기간(보통 1년)으로 구분하고, 구분된 기간에서의 최대값(또는 최소값)을 추출하고, 추출된 자료로부터 적합한 분포를 추정하는 과정으로 분류할 수 있다. (중략)

• Journal of Korea Water Resources Association
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• v.46 no.6
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• pp.643-653
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• 2013

The most important procedure in frequency analysis is to determine the appropriate probability distribution and to estimate quantiles for a given return period. To perform the frequency analysis, the goodness-of-fit tests should be carried out for judging fitness between obtained data from empirical probability distribution and assumed probability distribution. The previous goodness-of-fit could not consider enough extreme events from the recent climate change. In this study, the critical values of the modified Anderson-Darling test statistics were derived for 3-parameter Weibull distribution and power test was performed to evaluate the performance of the suggested test. Finally, this method was applied to 50 sites in South Korea. The result shows that the power of modified Anderson-Darling test has better than other existing goodness-of-fit tests. Thus, modified Anderson-Darling test will be able to act as a reference of goodness-of-fit test for 3-parameter Weibull model.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.369-370
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• 2012

일반적으로 회귀분석의 최적화는 평균적인 개념을 확장하여 사용되어지고 있다. 평균은 관찰값들에 관한 모든 정보와 관련된 통계량으로써 많은 연구에 이용되어지고 있다. 정규분포를 이루는 모집단의 경우 평균을 사용한 추정이 바람직하지만, 이상치로 인한 분포의 꼬리가 두꺼워지는 경우 중위수(median)를 사용하는 것이 바람직하다고 알려져 있다. 강수량의 분포형태는 꼬리(tail)가 두꺼운 왜곡된 형태를 갖고 있으므로 robust 통계량인 Quantile을 이용한 강수량의 분석 및 평가를 실시하였다. 본 연구에서는 Quantile에 따른 회귀선의 변화를 이용하여 강수량의 경향성을 평가하고, 극치강수량의 변화를 보여줄 수 있는 Quantle값을 추출해 보고자 한다. 또한 bootstrap 방법을 이용하여 Quantile에 따른 회귀계수의 신뢰구간을 분석하여 회귀인자의 신뢰성을 평가하였다. 본 연구에서 적용한 Quantile Regression 기법은 회귀계수의 추정에 있어서 회귀인자의 신뢰성을 Quantile-회귀계수 그래프를 통해 분석할 수 있으며, 이상값의 영향을 저감시키는 평균과 달리 이상값의 영향을 효과적으로 분리 및 재현시킬 수 있어 극치값에 따른 변화를 효과적으로 평가할 수 있으며, robust 통계량의 특징인 분산이 적은 안정적인 추정량을 확보할 수 있다.