• Magazine of the Korean Society of Agricultural Engineers
• /
• v.44 no.6
• /
• pp.49-60
• /
• 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. GEV distribution for the flood flow data of the applied watersheds was confirmed as the best one among others by the LH-moments ratio diagram and Kolmogorov-Smirnov test. Best fitting order of LH-moments will be derived by the confidence analysis of estimated design flood in the second report of this study.

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

• The Korean Journal of Applied Statistics
• /
• v.28 no.2
• /
• pp.269-279
• /
• 2015

This paper considers inferences of random effects. We show that the proposed confidence distribution (CD) performs well in logistic regression for random intercepts with small samples. Real data analyses are also done to identify the subject effects clearly.

• Proceedings of the Korean Society of Agricultural Engineers Conference
• /
• 2002.10a
• /
• pp.229-232
• /
• 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
• /
• 2005.10a
• /
• pp.284-287
• /
• 2005

The objective of this study is to check into variation trends of design rainfall according to change of the number of years for observed data. To make comparative study of the relation between design rainfall and recorded year, this study was used maximum rainfall for 24-hr consecutive duration at Gangneung, Seoul, Incheon, Chupungnyeong, Pohang, Daegu, Jeonju, Ulsan, Gwangju, Busan, Mokpo and Yeosu rainfall stations. The tests for Independence, Homogeneity and detection of outliers were used Wald-Wolfowitz's test, Mann-Whitney's test and Grubbs and Beck test respectively. To select appopriate distribution, the distribution of genaralized pareto(GPA), generalized extreme value(GEV), generalized logistic(GLO), lognormal and pearson type 3 distribution is judged by L-moment ratio diagram and Kolmogorov-Smirnov (K-S) test. Design rainfall was estimated by at-site frequency analysis using L-moments and Generalized extreme value(GEV) distribution according to change of the number of years for observed data. Through the comparative analysis for design rainfall induced by L-moments and GEV distribution, relationship between design rainfall and recorded year is provided.

• Journal of Korea Water Resources Association
• /
• v.50 no.3
• /
• pp.211-221
• /
• 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 Korea Academia-Industrial cooperation Society
• /
• v.10 no.5
• /
• pp.1009-1019
• /
• 2009

In this research, various characteristics of South Korea's design flood have been examined by deriving appropriate design flood, using data obtained from careful observation of actual floods occurring in selected main watersheds of the nation. 19 watersheds were selected for research in Korea. The various characteristics of annual rainfall were analyzed by using a moving average method. The frequency analysis was decided to be performed on the annual maximum flood of succeeding one year as a reference year. For the 19 watersheds, tests of basic statistics, independent, homogeneity, and outlier were calculated per period of annual maximum flood series. By performing a test using the LH-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test, among applied distributions of Gumbel (GUM), Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) distribution was found to be adequate compared with other probability distributions. Parameters of GEV distribution were estimated by L, L1, L2, L3 and L4-moment method based on the change in the order of probability weighted moments. Design floods per watershed and the periods of annual maximum flood series were derived by GEV distribution. According to the result of the analysis performed by using variation rate used in this research, it has been concluded that the time for changing the design conditions to ensure the proper hydraulic structure that considers recent climate changes of the nation brought about by global warming should be around the year 2002.

• Journal of Forest and Environmental Science
• /
• v.36 no.1
• /
• pp.7-16
• /
• 2020

Tree size distribution modelling is an integral part of forest management. Most distribution yield systems rely on some flexible probability models. In this study, a simple finite mixture of two components two-parameter Weibull distribution was compared with complex four-parameter distributions in terms of their fitness to predict tree size distribution of teak (Tectona grandis Linn f) plantations. Also, a system of equation was developed using Seemingly Unrelated Regression wherein the size distributions of the stand were predicted. Generalized beta, Johnson's SB, Logit-Logistic and generalized Weibull distributions were the four-parameter distributions considered. The Kolmogorov-Smirnov test and negative log-likelihood value were used to assess the distributions. The results show that the simple finite mixture outperformed the four-parameter distributions especially in stands that are bimodal and heavily skewed. Twelve models were developed in the system of equation-one for predicting mean diameter, seven for predicting percentiles and four for predicting the parameters of the finite mixture distribution. Predictions from the system of equation are reasonable and compare well with observed distributions of the stand. This simplified mixture would allow for wider application in distribution modelling and can also be integrated as component model in stand density management diagram.

• Journal of The Korean Society of Agricultural Engineers
• /
• v.51 no.3
• /
• pp.53-62
• /
• 2009

This study was carried out to select optimal probability distribution based on design accumulated monthly mean inflow from the viewpoint of drought by Gamma (GAM), Generalized extreme value (GEV), Generalized logistic (GLO), Generalized normal (GNO), Generalized pareto (GPA), Gumbel (GUM), Normal (NOR), Pearson type 3 (PT3), Wakeby (WAK) and Kappa (KAP) distributions for the observed accumulative monthly mean inflow of Chungjudam. L-moment ratio was calculated using observed accumulative monthly mean inflow. Parameters of 10 probability distributions were estimated by the method of L-moments with the observed accumulated monthly mean inflow. Design accumulated monthly mean inflows obtained by the method of L-moments using different methods for plotting positions formulas in the 10 probability distributions were compared by relative mean error (RME) and relative absolute error (RAE) respectively. It has shown that the design accumulative monthly mean inflow derived by the method of L-moments using Weibull plotting position formula in WAK and KAP distributions were much closer to those of the observed accumulative monthly mean inflow in comparison with those obtained by the method of L-moment with the different formulas for plotting positions in other distributions from the viewpoint of RME and RAE.

• Journal of the Korean Society of Marine Environment & Safety
• /
• v.21 no.3
• /
• pp.253-258
• /
• 2015

The purpose of this study is to find suitable probability distribution function of complex distribution data like multimodal. Normal distribution is broadly used to assume probability distribution function. However, complex distribution data like multimodal are very hard to be estimated by using normal distribution function only, and there might be errors when other distribution functions including normal distribution function are used. In this study, we experimented to find fit probability distribution function in multimodal area, by using AIS(Automatic Identification System) observation data gathered in Mokpo port for a year of 2013. By using chi-squared statistic, gaussian mixture model(GMM) is the fittest model rather than other distribution functions, such as extreme value, generalized extreme value, logistic, and normal distribution. GMM was found to the fit model regard to multimodal data of maritime traffic flow distribution. Probability density function for collision probability and traffic flow distribution will be calculated much precisely in the future.