• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.1137-1141
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• 2004

본 연구에서는 Probability Weighted Moments의 새로운 선형조합기법인 LQ-moments를 이용하여 GEV 분포의 매개변수를 추정하고 L, LH, LQ-moments를 사용하여 뉴욕주의 Donnattsburg에 위치한 Independence River의 홍수량을 빈도 해석하였다. LH, LQ-moments가 제시된 근본적인 이유는 L-moments가 극치값에 내해 지나치게 민감한 단점을 보완하기 위해서인데, 이번 연구의 결과에 의하면 오히려 LH, LQ-moments가 극치값에 대해 민감하게 반응하여 부정확한 결과가 도출되었다. 그러므로 항상 LH, LQ-moments가 L-moments의 대안이 될 수 있는 것은 아님을 알게 되었다. 그리고 수학적 유도에서 L, LH, LQ-moments는 좀더 쉽고 간편한 메개변수 추정을 위해 Probability Weighted Moments의 선형조합을 통해 고안되었다는 공통점을 가지고 있지만, 이 점을 제외한 나머지 부분의 수식 유도에서는 서로 많은 차이가 있어서 지역적인 특성과 확률분포형의 특성을 고려하여 L, LH, LQ-moments 중에서 선별 사용해야 할 것이다.

• 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.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3B
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• pp.259-267
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• 2009

Generalized Extreme Value (GEV) distribution is recommended for flood frequency and extreme rainfall distribution in many country. L-moment method is the most common estimation procedure for the GEV distribution. In this study, the relationships between the cross-site correlations between extreme events and the cross-correlation of estimators of L-moment ratios (L-moment Coefficient of Variation (L-CV) and L-moment Coefficient of Skewness (L-CS)) for data generated from GEV distribution were derived by Monte Carlo simulation. Those relationships were fit to the simple power function. In this Monte Carlo simulation, GEV+ distribution were employed wherein unrealistic negative values were excluded. The simple power models provide accurate description of the relationships between cross-correlation of data and cross-correlation of L-moment ratios. Estimated parameters and accuracies of the power functions were reported for different GEV distribution parameters combinations. Moreover, this study provided a description about regional regression approach using Generalized Least Square (GLS) regression method which require the cross-site correlation among L-moment estimators. The relationships derived in this study allow regional GLS regression analyses of both L-CV and L-CS estimators that correctly incorporate the cross-correlation among GEV L-moment estimators.

• Proceedings of the Korea Water Resources Association Conference
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• 1996.05a
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• pp.259-267
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• 1996

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.285-294
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• 2005

This paper deals with the comparison of parameter estimation methods in a 3-parameter Kappa distribution which is sometimes used in flood frequency analysis. Method of moment estimation(MME), L-moment estimation(L-ME), and maximum likelihood estimation(MLE) are applied to estimate three parameters. The performance of these methods are compared by Monte-carlo simulations. Especially for computing MME and L-ME, three dimensional nonlinear equations are simplified to one dimensional equation which is calculated by the Newton-Raphson iteration under constraint. Based on the criterion of the mean squared error, L-ME (or MME) is recommended to use for small sample size( n$\le$100) while MLE is good for large sample size.

• Proceedings of the Korea Water Resources Association Conference
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• 2007.05a
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• pp.321-325
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• 2007

3개의 매개변수(location, scale, shape)로 이루어진 GEV와 GLO 분포는, 미국의 공식적인 홍수빈도 분포인 Log Pearson Type III와 함께 수문분야에서 중요한 위치를 차지하고 있다. 본 연구에서는 Monte Carlo 실험을 이용하여 GEV와 GLO 분포에서 서로 다른 두 지점의 유출량 자료를 생성하여 L-CV(L-moment Coefficient of Variation; $\tau_2$)와 L-CS(L-moment Coefficient of Skewness; $\tau_3$)를 추정하였으며, L-moment 추정값들 간의 교차상관$(\tau_2-\tau_2,\;\tau_3-\tau_3,\;\tau_2-\tau_3)$과 유출량 자료간의 교차상관의 관계를 Simple Power 함수를 이용하여 유도하였다. 실험 과정에서 GEV와 GLO 분포가 비현실적인 음수 유출량을 생성하여, 실험 결과에 큰 영향이 있음을 확인하여, 두 분포에서 생성된 유출량 자료에서 음수값을 제외한 GEV+와 GLO+ 분포를 이용하여 관계식을 유도하고 이를 GEV와 GLO 분포의 결과와도 비교하였다. 본 연구에서 도출된 관계식은 향후 Generalized Least Square 회귀식을 이용하여 홍수분포의 지역 매개변수를 추정하기 위해 활용성이 클 것으로 기대한다.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.1103-1106
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• 2004

The objective of this study is to induce the design drought rainfall by the methodology of L-moment including testing homogeneity, independence and outlier of the data of annual minimum monthly rainfall in 57 rainfall stations in Korea in terms of consecutive duration for 1, 2, 4, 6, 9 and 12 months. To select appropriate distribution of the data for annual minimum monthy rainfall by rainfall station, the distribution of generalized extreme value (GEV), generalized logistic (GLO) as well as that of generalized pareto (GPA) are applied and the appropriateness of the applied GEV, GLO, and GPA distribution is judged by L-moment ratio diagram and Kolmogorov-Smirnov (K-S) test. As for the annual minimum monthly rainfall measured by rainfall station and that stimulated by Monte Carlo techniques, the parameters of the appropriately selected GEV and GPA distributions are calculated by the methodology of L-moment and the design drought rainfall is induced. Through the comparative analysis of design drought rainfall induced by GEV and GPA distribution by rainfall station, the optimal design drought rainfall by rainfall station is provided.

• Journal of the Korea institute for structural maintenance and inspection
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• v.7 no.4
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• pp.91-97
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• 2003

The maximum moment may occur at interior supports of continuous bridges. If the bigger moment is applied on them, a local yielding at interior supports may occur. They may show plastic behaviors, and the moment will be redistributed. The strength design, L.F.D., redistributes 10% of the negative moment which is obtained from the elastic analysis. However, A.L.F.D method computes the moment which is redistributed. This moment is called automoment. The moment-rotation curve is needed to find automoment. In this paper moment-rotation curve for compact sections suggested from AASHTO Guide Specifications is used to find automoment. Based on A.L.F.D. limit states specification method, a three-span continuous bridge is designed.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2002.10a
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• pp.225-228
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• 2002

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 in 38 Korean rainfall stations. To select the fit appropriate distribution of annual maximum daily rainfall data according to rainfall stations, applied were Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) probability distributions were applied. and their aptness was judged Dusing an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test, the aptitude was judged of applied distributions such as GEV, GLO and GPA. The GEV and GLO distributions were selected as the appropriate distributions. Their parameters were estimated Targetingfrom the observed and simulated annual maximum daily rainfalls and using Monte Carlo techniques, the parameters of GEV and GLO selected as suitable distributions were estimated and. dDesign rainfallss were then derived, using the L-moment. Appropriate design rainfalls were suggested by doing a comparative analysis of design rainfall from the GEV and GLO distributions according to rainfall stations.