• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.501-505
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• 2012

In this paper, general classes of continuous distributions are characterized by considering the conditional expectations of functions of upper record statistics. The specific distribution considered as a particular case of the general class of distribution are Exponential, Exponential Power(EP), Inverse Weibull, Beta Gumbel, Modified Weibull(MW), Weibull, Pareto, Power, Singh-Maddala, Gumbel, Rayleigh, Gompertz, Extream value 1, Beta of the first kind, Beta of the second kind and Lomax.

• Journal of Korea Water Resources Association
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• v.50 no.4
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• pp.253-261
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• 2017

A lot of nonstationary frequency analyses have been studied in recent years as the nonstationarity occurs in hydrologic time series data. In nonstationary frequency analysis, various forms of probability distributions have been proposed to consider the time-dependent statistical characteristics of nonstationary data, and various methods for parameter estimation also have been studied. In this study, we aim to introduce a parameter estimation method for nonstationary Gumbel distribution using ensemble empirical mode decomposition (EEMD); and to compare the results with the method of maximum likelihood. Annual maximum rainfall data with a trend observed by Korea Meteorological Administration (KMA) was applied. As a result, both EEMD and the method of maximum likelihood selected an appropriate nonstationary Gumbel distribution for linear trend data, while the EEMD selected more appropriate nonstationary Gumbel distribution than the method of maximum likelihood for quadratic trend data.

• 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.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.85-95
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• 2012

In this paper we define extended negative quadrant dependence which is weaker negative quadrant dependence and show conditions for having extended negative quadrant dependence property. We also derive generalized Farlie-Gumbel-Morgenstern uniform distributions that possess the extended quadrant dependence property.

• Journal of Korea Water Resources Association
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• v.45 no.8
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• pp.827-837
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• 2012

The estimation of the rainfall quantile is of great importance in designing hydrologic structures. Conventionally, the rainfall quantile is estimated by univariate frequency analysis with an appropriate probability distribution. There is a limitation in which duration of rainfall is restrictive. To overcome this limitation, bivariate frequency analysis by using 3 copula models is performed in this study. Annual maximum rainfall events in 5 stations are used for frequency analysis and rainfall depth and duration are used as random variables. Gumbel (GUM), generalized logistic (GLO) distributions are applied for rainfall depth and generalized extreme value (GEV), GUM, GLO distributions are applied for rainfall duration. Copula models used in this study are Frank, Joe, and Gumbel-Hougaard models. Maximum pseudo-likelihood estimation method is used to estimate the parameter of copula, and the method of probability weighted moments is used to estimate the parameters of marginal distributions. Rainfall quantile from this procedure is compared with various marginal distributions and copula models. As a result, in change of marginal distribution, distribution of duration does not significantly affect on rainfall quantile. There are slight differences depending on the distribution of rainfall depth. In the case which the marginal distribution of rainfall depth is GUM, there is more significantly increasing along the return period than GLO. Comparing with rainfall quantiles from each copula model, Joe and Gumbel-Hougaard models show similar trend while Frank model shows rapidly increasing trend with increment of return period.

• 한국신재생에너지학회:학술대회논문집
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• 2010.11a
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• pp.189.1-189.1
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• 2010

The wind farm where the wind velocity condition is excellent and economical can be established to produce power with the multiple wind power turbine. The wind velocity which is suitable to Wind Power Development must be evaluated for searching the economical wind farm on planning the wind farm. In this paper, based on wind speed data at 24 locations in Korea from 1971 through 2009, the basic wind velocity which can be applied to designing wind power development is estimated using the statiscal process. The wind velocity which is measured from observation stations is revised according to wind gauge's height and Circumferential environment. The wind speeds for 200 year's return period in 24 locations are determined using the Gumbel's distribution.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.647-658
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• 2009

It is already known from the previous study that flood seems to have heavier tail. Therefore, to make prediction of future extreme label, some agreement of tail behavior of extreme data is highly required. The LH-moments estimation method, the generalized form of L-moments is an useful method of characterizing the upper part of the distribution. LH-moments are based on linear combination of higher order statistics. In this study, we have formulated LH-moments of five distributions useful in hydrology such as, two types of three parameter kappa distributions, beta-${\kappa}$ distribution, beta-p distribution and a generalized Gumbel distribution. Using LH-moments reduces the undue influences that small sample may have on the estimation of large return period events.

• Structural Engineering and Mechanics
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• v.49 no.3
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• pp.355-372
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• 2014

Considering the history of severe earthquakes and the presence of active faults in the greater Tehran region, the possibility of a destructive earthquake occurring is high and seismic hazard analysis is crucial. Gumbel distributions are commonly-used statistical distributions in earthquake engineering and seismology. Their main advantage is their basis on the largest earthquake magnitudes selected from an equal-time predefined set. In this study, the first asymptotic distribution of extremes is used to estimate seismicity parameters and peak ground acceleration (PGA). By assuming a Poisson distribution for the earthquakes, after estimation of seismicity parameters, the mean return period and the probable maximum magnitude within a given time interval are obtained. A maximum probable magnitude of 7.0 has a mean return period of 100 years in this region. For a return period of 475 years, the PGA in the greater Tehran region is estimated to be 0.39g to 0.42g, depending on local site conditions. This value is greater than that of the Iranian Code for Seismic Design of Buildings, indicating that a revision of the code is necessary.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.327-331
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• 2012

본 연구에서는 실무에서 적용하고 있는 매개변수 산정방법인 L-moment 방법과 자료계열의 이상치를 고려하여 수정 제시된 TL-moment 방법을 비교 분석하여 빈도해석을 수행하는 경우, 보다 효율적인 매개 변수 산정방법으로 수공구조물 설계 및 재난방재계획에 합리적인 기준을 제시하고자 하였다. 산정방법의 비교를 위하여 서울특별시를 대상으로 강우자료를 수집하였으며, 국내 강우에 적합한 확률분포형으로 선정되어 있는 Gumbel 분포형에 적용하여 모멘트와 확률강우량을 산정하였다. 또한, 산정된 모멘트와 지속기간 25개, 재현기간 8개년의 확률강우량을 비교하여 타당성을 검토하였다. 본 연구의 수행으로 TL-moment 방법에 의한 모멘트의 변동폭이 L-moment 방법 보다 작게 산정되었으며, 산정된 확률강우량의 비교에서 이 상치의 보정이 확인되었다.

• Proceedings of the Korea Water Resources Association Conference
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• 2018.05a
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• pp.312-312
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• 2018

우리나라의 기후 지형적 특성에 따라 연강수량의 50% 이상이 여름철에 내리며 이러한 짧은 기간에 집중적으로 내리는 강수패턴 조건하에서 수공구조물 설계시 대부분 극치빈도분석을 활용한다. 우리나라의 경우 단일 Gumbel 분포를 활용한 극치빈도분석을 많이 이용한다. 하지만, 최근 이상기후로 인하여 전세계적으로 강수패턴의 특징이 급격히 변하고 있으며, 우리나라의 강수패턴 또한 바뀌어가고 있다. 연강수량의 대부분은 태풍과 장마로 인한 강수량으로 이루어져 있고, 일반적으로 두 개의 모집단으로 이루어진 형태를 보인다. 앞선 연구에서 두 개 이상의 첨두를 가지는 형태의 연최대강수량 자료에 대해 8개의 지속시간별(1, 2, 3, 6, 9, 12, 18, 24hr)로 Bayesian 기법의 단일 Gumbel 분포형과 혼합 Gumbel분포형 기반의 극치빈도분석 결과를 비교하였고, 혼합 Gumbel 분포형이 이중첨두 부분의 거동을 효과적으로 모의하는 것을 확인하였다. 본 연구에서는 이상기후로 인한 강수량의 특징의 급격한 변화에 일정한 패턴이 있음을 가정하고 이중첨두의 연 최대일강수량 자료에 대해 혼합 Gumbel 분포형 기반 비정상성 빈도분석을 실시하였다. 정상성 빈도분석과의 비교를 위해 확률분포의 매개변수 산정시 우도함수를 Bayesian 기법을 통해 산정하여 각 분포형의 Bayesian information criterion(BIC) 값을 비교하였다. 비정상성일 경우의 BIC 값이 정상성일 경우 보다 작게 산정되었고, 강수패턴이 경향성을 가지는 것으로 판단할 수 있었다. 비정상성 혼합 Gumbel 분포형 모델은 최근 급격한 강수패턴의 변화에 대한 대응책으로서 활용성이 높을 것으로 기대된다.