• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.65-81
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• 2024

In this paper, we announce that the strategy of comparing the complex moments of L(1, χ_u) to that of a random Euler product L(1, 𝕏) is also valid in even characteristic case. We give an asymptotic formulas for the complex moments of L(1, χ_u) in a large uniform range. We also give Ω-results for the extreme values of L(1, χ_u).

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1998.10a
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• pp.331-337
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• 1998

This study was carried out to derive optimal design floods by Weibull-3 distribution with the annual maximum series at seven watersheds along Man, Nagdong, Geum, Yeongsan and Seomjin river systems. Adequacy for the analysis of flood data used in this study was acknowledged by the tests of Independence, Homogeneity, detection of Outliers. 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 Weibull-3 distribution were compared by the rotative mean error and relative absolute error. It has shown that design floods derived by the method of L-moments using Weibull plotting position formula in Weibull-3 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.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2002.10a
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• pp.237-240
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• 2002

Design rainfall using LH-moments following the consecutive duration were derived by the regional and at-site analysis using the observed and simulated data resulted from Monte Carlo techniques. RRMSE, RBIAS and RR in RRMSE for the design rainfall were computed and compared in the regional and at-site frequency analysis. Consequently, it was shown that the regional analysis can substantially more reduce the RRMSE, RBIAS and RR in RRMSE than at-site analysis in the prediction of design rainfall. RE for an optimal order of L-moments was also computed by the methods of L, L1, L2, L3 and L4-moments for GEV distribution. It was found that the method of L-moments is more effective than the others for getting optimal design rainfall according to the regions and consecutive durations in the regional frequency analysis. Diagrams for the design rainfall derived by the regional frequency analysis using L-moments were drawn according to the regions and consecutive durations by GIS techniques.

• Magazine of the Korean Society of Agricultural Engineers
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• v.44 no.5
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• pp.41-53
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• 2002

This study was conducted to derive the regional design rainfall by the regional frequency analysis based on the regionalization of the precipitation suggested by the first report of this project. According to the regions and consecutive durations, optimal design rainfalls were derived by the regional frequency analysis for L-moment in the second report of this project. Using the LH-moment ratios and Kolmogorov-Smirnov test, the optimal regional probability distribution was identified to be the Generalized extreme value (GEV) distribution among applied distributions. regional and at-site parameters of the GEV distribution were estimated by the linear combination of the higher probability weighted moments, LH-moment. Design rainfall using LH-moments following the consecutive duration were derived by the regional and at-site analysis using the observed and simulated data resulted from Monte Carlo techniques. Relative root-mean-square error (RRMSE), relative bias (RBIAS) and relative reduction (RR) in RRMSE for the design rainfall were computed and compared in the regional and at-site frequency analysis. Consequently, it was shown that the regional analysis can substantially more reduce the RRMSE, RBIAS and RR in RRMSE than at-site analysis in the prediction of design rainfall. Relative efficiency (RE) for an optimal order of L-moments was also computed by the methods of L, L1, L2, L3 and L4-moments for GEV distribution. It was found that the method of L-moments is more effective than the others for getting optimal design rainfall according to the regions and consecutive durations in the regional frequency analysis. Diagrams for the design rainfall derived by the regional frequency analysis using L-moments were drawn according to the regions and consecutive durations by GIS techniques.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2002.10a
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• pp.229-232
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• 2002

This study was conducted to estimate the design flood by the determination of best fitting order of LH-moments of the annual maximum series at six and nine watersheds in Korea and Australia, respectively. Adequacy for flood flow data was confirmed by the tests of independence, homogeneity, and outliers. Gumbel (GUM), Generalized Extreme Value (GEV), Generalized Pareto (GPA), and Generalized Logistic (GLO) distributions were applied to get the best fitting frequency distribution for flood flow data. Theoretical bases of L, L1, L2, L3 and L4-moments were derived to estimate the parameters of 4 distributions. L, L1, L2, L3 and L4-moment ratio diagrams (LH-moments ratio diagram) were developed in this study.

• 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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.41 no.4
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• pp.25-29
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• 1999

This study was conducted to derive optimal design floods by Gerneralized Extreme Value(GEV) and Weibull-3 distributions for the annual maximum series at ten watersheds along Han,Nagdong, Geum, Yeongsan and Seomjin reiver systems. Adequency for the analysis of flood data used in this study was established by the tests of Independence. Homogeneity , detection of Outlines, L-moments. Design flood sobtaine dby /methods of Moments and L-Moments using different methods for plotting positions in BEV and Weibull-3 distributions were compared by the Relative Mean Errors(RME) and Root MEan Square Errors(RMSE). The result wa found that design floods derived by the L-moments using the other formulas for plotting positions from the viewpoint of Relative Mean Errors and Root Mean Square Errors.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.1-12
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• 2022

In this paper we prove an even characteristic analogue of the result of Andrade on lower bounds for moment of quadratic Dirichlet L-functions in odd characteristic. We establish lower bounds for the moments of Dirichlet L-functions of characters defined by Hasse symbols in even characteristic.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1007-1014
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• 2012

We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point 1/2.

• 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.