• Water Engineering Research
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• v.4 no.3
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• pp.155-173
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• 2003

Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

• 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.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.421-441
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• 2017

In this survey, estimation methods for structural vector autoregressive models are presented in a systematic way. Both frequentist and Bayesian methods are considered. Depending on the model setup and type of restrictions, least squares estimation, instrumental variables estimation, method-of-moments estimation and generalized method-of-moments are considered. The methods are presented in a unified framework that enables a practitioner to find the most suitable estimation method for a given model setup and set of restrictions. It is emphasized that specifying the identifying restrictions such that they are linear restrictions on the structural parameters is helpful. Examples are provided to illustrate alternative model setups, types of restrictions and the most suitable corresponding estimation methods.

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.377-383
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• 2020

The likelihood-based inference in a nonlinear generalized mixed model often requires computing moments of truncated multivariate normal random variables. Many methods have been proposed for the computation using a recurrence relation or the moment generating function; however, these methods rely on high dimensional numerical integrations. The numerical method is known to be inefficient for high dimensional integral in accuracy. Besides the accuracy, the methods demand too much computing time to use them in practical analyses. In this note, a moment calculation method is proposed under an assumption of a certain covariance structure that occurred mostly in generalized mixed models. The method needs only low dimensional numerical integrations.

• 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.

• 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.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.463-477
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• 2009

Parameter estimation methods such as maximum likelihood estimation method, probability weighted moments method, regression method have been popularly applied to various extreme value models in numerous literature. Among three methods above, the performance of regression method has not been rigorously investigated yet. In this paper the regression method is compared with the other methods via Monte Carlo simulation studies for estimation of parameters of the Generalized Extreme Value(GEV) distribution and the Generalized Pareto(GP) distribution. Our simulation results indicate that the regression method tends to outperform other methods under small samples by providing smaller biases and root mean square errors for estimation of location parameter of the GEV model. For the scale parameter estimation of the GP model under small samples, the regression method tends to report smaller biases than the other methods. The regression method tends to be superior to other methods for the shape parameter estimation of the GEV model and GP model when the shape parameter is -0.4 under small and moderately large samples.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.15-27
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• 2018

Parametric method of flood frequency analysis involves fitting of a probability distribution to observed flood data. When record length at a given site is relatively shorter and hard to apply the asymptotic theory, an alternative distribution to the generalized extreme value (GEV) distribution is often used. In this study, we consider the beta-P distribution (BPD) as an alternative to the GEV and other well-known distributions for modeling extreme events of small or moderate samples as well as highly skewed or heavy tailed data. The L-moments ratio diagram shows that special cases of the BPD include the generalized logistic, three-parameter log-normal, and GEV distributions. To estimate the parameters in the distribution, the method of moments, L-moments, and maximum likelihood estimation methods are considered. A Monte-Carlo study is then conducted to compare these three estimation methods. Our result suggests that the L-moments estimator works better than the other estimators for this model of small or moderate samples. Two applications to the annual maximum stream flow of Colorado and the rainfall data from cloud seeding experiments in Southern Florida are reported to show the usefulness of the BPD for modeling hydrologic events. In these examples, BPD turns out to work better than $beta-{\kappa}$, Gumbel, and GEV distributions.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.877-883
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• 2013

The quadratic inference functions (QIF) method proposed by Qu et al. (2000) and the generalized method of moments (GMM) for marginal regression analysis of longitudinal data with time-dependent covariates proposed by Lai and Small (2007) both are the methods based on generalized method of moment (GMM) introduced by Hansen (1982) and both use generalized estimating equations (GEE). Lai and Small (2007) divided time-dependent covariates into three types such as: Type I, Type II and Type III. In this paper, we compared these methods in the case of Type II and Type III in which full covariates conditional mean assumption (FCCM) is violated and interested in whether they can improve the results of GEE with independence working correlation. We show that in the marginal regression model with Type II time-dependent covariates, GMM Type II of Lai and Small (2007) provides more ecient result than QIF and for the Type III time-dependent covariates, QIF with independence working correlation and GMM Type III methods provide the same results. Our simulation study showed the same results.

• 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.