• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.239-239
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• 2015

This study presents a bivariate extension of the goodness-of-fit measure for regional frequency distributions developed by Hosking and Wallis [1993] for use with the method of L-moments. Utilising the approximate joint normal distribution of the regional L-skewness and L-kurtosis, a graphical representation of the confidence region on the L-moment diagram can be constructed as an ellipsoid. Candidate distributions can then be accepted where the corresponding the oretical relationship between the L-skewness and L-kurtosis intersects the confidence region, and the chosen distribution would be the one that minimises the Mahalanobis distance measure. Based on a set of Monte Carlo simulations it is demonstrated that the new bivariate measure generally selects the true population distribution more frequently than the original method. An R-code implementation of the method is available for download free-of-charge from the GitHub code depository and will be demonstrated on a case study of annual maximum series of peak flow data from a homogeneous region in Italy.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.3
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• pp.45-55
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• 2000

This study was carried out to derive optimal design low flows bythe Weibull-3 and Wakeby distributions for the partial consecutive duration series at seven watersheds along Han. nagdong, Geum Yeongsan and Seomjin river systems. L-coefficient of variation L-skewness and L-kurtosis were calculated by the L-moment ratio respectively. Parameters were estimated by the method of L-Moments with consecutive duration. Design low flows obtained by method of L-Moments using with consecutive duration, Design low flows obtained by method of L-Moments using different methods for plotting positions formulas in the Weibull-3 and Wakeby distributions were compared by the Root Mean Square Errors(RMSE). It has shown that design low flows derived by the method of L-moments using Weivull plotting position formula in Wakeby distribution were much closer to those of the observed data in comparison with those obtained by the methods of L-moments with the different formulas for plotting positions in Weibull-3 distribution from the viewpoint of Root Mean Square Errors.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.531-536
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• 1999

This study was carried out to derive optimal design drought flows by the Weibull-3 and Wakeby distributions for the annual drought flows series at seven watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. L-coefficient of variation , L-skewness and L-kurtosis were calculated by the L-moment ratio respectivley. Parameters were estimated by the Methods o fL-Moments with continuous duration. Design drought flows obtained by Methods of L-Moments using Weibull plotting positions formula in the Weibull-3 and Wakeby distributions were compared by the Relative Mean Errors(RME), Relative Absolute Errors (RAE) and Root Mean Square Errors(RMSE). It has shown that design drought flows by the Wakeby distribution using method of L-moments are much closer to those of the observed data in comparison with those obtained by the Weibull-3 distribution using method of L-moments.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1998.10a
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• pp.318-324
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• 1998

This study was conducted to derive optimal design floods by Generalized Extreme-value(GEV) distribution for the annual maximum series at ten watersheds along Han, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was established by the tests of Independence, Homogeneity, detection of Outliers. L-coefficient of variation, L-skewness and L-kurtosis were calculated by L-moment ratio respectively. Parameters were estimated by the Methods of Moments and L-Moments. Design floods obtained by Methods of Moments and L-Moments using different methods for plotting positions in GEV distribution were compared by the relative mean and relative absolute error. It was found that design floods derived by the method of L-moments using weibull plotting position formula in GEV distribution are much closer to those of the observed data in comparison with those obtained by method of moments using different formulas for plotting positions in view of relative mean and relative absolute error.

• 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.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.143-152
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• 2002

In an effort to make a right choice among ratio estimation strategies and PPS sampling strategies, we conduct an empirical investigation of the relative performances of three ratio estimation strategies and four PPS estimation strategies using a set of 12 natural populations. The quality of a strategy is measured in the traditional way, namely with the consideration of efficiency, achieved coverage rate of the nominal 99% confidence interval and approach to normality (asymmetry).

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.3
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• pp.41-50
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• 1999

Derivatio of reasonable design floods was attempted by comparative analysis of design floods derived by Generalized Extreme Value(GEV) distribution using methods of L-moments and LH-moments for the annual maximum series at ten watersheds along Han, Nagdong. Geum, Yeongsan and Seomjin river systems, LH-coefficient of variation, LH-skewness and Lh-kurtosis were calcualted by KH-moment ration respectively. Paramenters were estimated by the Method of LH-Moments, Design floods obtained by Method of LH-Moments using different methods for plotting positionsi n GEV distribution and design floods were compared with those obtained using the Method of L-Moments by the Relative Mean Errors(RME) and Relative Absolute Errors(RAE). The results was found that design floods derived by the method of L-Moments and LH-Moments using Cunnane plotting position formula in the GEV distribution are much closer to those of the observed data in comparison with those obtained by methods of L-moments and LH-moments using the other formula for plotting positions from the viewpoint of Relative Mean Errors and Relative Absolute Errors. In viewpoint of the fact that hydrqulic structures including dams and levees are genrally using design floods with the return period of two hundred years or so, design floods derived by LH-Moments are seemed to be more reasonable than those of L-Moments in the GEV distribution.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.479-485
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• 1999

This study was conducted to derived design floods by Generalized Extreme Value(GEV) distributiion for the annual maximum series at ten watersheds along Han, Nagdong, Geum , Yeongsan and Seomjin river systems. Adequency for the analysis of flood data used in this study was established by the test of Independence, Homogeneity , detection of Outliers. Coefficient of variation , skewness and kurtosis were calculated by the L-Moment, and LH-Moment ratio respectively. Parameters were estimated by the Method of L-Method of LH-Moment. Design floods obtained by Method of L-Moments and LH-Moments using different methods for plotting positions in GEV distributions and were compared with those obatined using the Method of L-Moments and LH-Moments by the Relative Mean Errors and Realtive Absoulte Errors. It was found that desgin floods derived by the method of L-Moments and LH-Moments using Cunnane plotting position foumula in the GEV distribution are much closer to those of the observed data in comparison with those obtained by methods of L-moments and LH-moments using the other formula for poltting postions from the viewpoint of Relative Mean Errors and Relative Absoulte Errors. In view of the fact that hydraulic structures indcluding dams and levees are generally usiong design floods with the return period of two hundred years or so, design floods derived by LH-Moments are seemed to be more reasonable than those of L-Moments in the GEV distribution.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.11C
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• pp.1073-1078
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• 2007

In this paper, we propose an iterative mixed norm image restoration algorithm using multi regularization parameters. A functional which combines the regularized $l_2$ norm functional and the regularized $l_4$ norm functional is proposed to efficiently remove arbitrary noise. The smoothness of each functional is determined by the regularization parameters. Also, a regularization parameter is used to determine the relative importance between the regularized $l_2$ norm functional and the regularized $l_4$ norm functional using kurtosis. An iterative algorithm is utilized for obtaining a solution and its convergence is analyzed. Experimental results demonstrate the capability of the proposed algorithm.

• Journal of Environmental Science International
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• v.8 no.4
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• pp.431-441
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• 1999

In this study, the regional frequency analysis is used to determine each subbasin drought frequency with reliable monthly precipitation and the L-Moments method which is almost unbiased and has very nearly a normal distribution is used for the parameter estimation of monthly precipitation time series in Nakdong river basin. As the result of this study, the duration of '93-'94 is most severe drought year than any other water year and the drought frequency is established as compared the regional frequency analysis result of cumulative precipitation of 12th duration months in each subbasin with that of 12th duration months in the major drought duration. The Linear regression equation is induced according to linear regression analysis of drought frequency between Nakdong total basin and each subbasin of the same drought duration. Therefore, as the foundation of this study, it can be applied proposed method and procedure of this study to the water budget analysis considering safety standards for the design of impounding facilities large-scale river basin and for this purpose, above all, it is considered that expansion of reliable preciptation data is needed in watershed rainfall station.