• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1107-1117
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• 2005

We consider the problem of estimating the scale and shape parameters in the Weibull distribution based on censored samples. We propose the approximate maximum likelihood estimators (AMLEs) of the scale and shape parameters in the Weibull distribution based on Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error (MSE).

• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1549-1566
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• 2016

Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.

• Journal of Wetlands Research
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• v.13 no.3
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• pp.499-514
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• 2011

An underlying assumption of traditional hydrologic frequency analysis is that climate, and hence the frequency of hydrologic events, is stationary, or unchanging over time. Under stationary conditions, the distribution of the variable of interest is invariant to temporal translation. Water resources infrastructure planning and design, such as dams, levees, canals, bridges, and culverts, relies on an understanding of past conditions and projection of future conditions. But, Water managers have always known our world is inherently non-stationary, and they routinely deal with this in management and planning. The aim of this paper is to give a brief introduction to non-stationary extreme value analysis methods. In this paper, a non-stationary hydrologic frequency analysis approach is introduced in order to determine probability rainfall consider changing climate. The non-stationary statistical approach is based on the conditional Generalized Extreme Value(GEV) distribution and Maximum Likelihood parameter estimation. This method are applied to the annual maximum 24 hours-rainfall. The results show that the non-stationary GEV approach is suitable for determining probability rainfall for changing climate, sucha sa trend, Moreover, Non-stationary frequency analyzed using SOI(Southern Oscillation Index) of ENSO(El Nino Southern Oscillation).

• Wind and Structures
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• v.16 no.4
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• pp.355-372
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• 2013

The Gringorten estimator has been extensively used in extreme value analysis of wind speed records to obtain unbiased estimates of design wind speeds. This paper reviews the derivation of the Gringorten estimator for the mean plotting position of extremes drawn from parents of the exponential type and demonstrates how it eliminates most of the bias caused by the classical Weibull estimator. It is shown that the coefficients in the Gringorten estimator are the asymptotic values for infinite sample sizes, whereas the estimator is most often used for small sample sizes. The principles used by Gringorten are used to derive a new Consistent Linear Unbiased Estimator (CLUE) for the mean plotting positions for the Fisher Tippett Type 1, Exponential and Weibull distributions and for the associated standard deviations. Analytical and Bootstrap methods are used to calibrate the bias error in each of the estimators and to show that the CLUE are accurate to better than 1%.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.3
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• pp.31-42
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• 2004

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 at 38 rainfall stations in Korea. To select the appropriate distribution of annual maximum daily rainfall data by the rainfall stations, Generalized Extreme Value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO) and Pearson Type 3 (PT3) probability distributions were applied and their aptness were judged using an L-moment ratio diagram and the Kolmogorov-Smirnov (K-S) test. Parameters of appropriate distributions were estimated from the observed and simulated annual maximum daily rainfall using Monte Carlo techniques. Design rainfalls were finally derived by GEV distribution, which was proved to be more appropriate than the other distributions.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2001.10a
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• pp.319-323
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• 2001

This study was conducted to derive the regional design rainfall by the regional frequency analysis based on the regionalization of the precipitation. Using the L-moment ratios and Kolmogorov-Smirnov test, the underlying regional probability distribution was identified to be the Generalized extreme value distribution among apt]lied distributions. regional and at-site parameters of the Generalized extreme value distribution were estimated by the method of L-moment. The regional and at-site analysis for the design rainfall were tested by Monte Carlo simulation. Relative root-mean-square error(RRMSE), relative bias(RBIAS) and relative reduction(RR) in RRMSE were computed and compared with those resulting from at-site Monte Carlo simulation. All show that the regional analysis procedure can substantially reduce the RRMSE, RBIAS and RR in RRMSE in the prediction of design rainfall. Consequently, optimal design rainfalls following the regions and consecutive durations were derived by the regional frequency analysis.

• Magazine of the Korean Society of Agricultural Engineers
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• v.43 no.5
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• pp.70-82
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• 2001

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. Using the L-moment ratios and Kolmogorov-Smirnov test, the underlying regional probability distribution was identified to be the Generalized extreme value distribution among applied distributions. Regional and at-site parameters of the generalized extreme value distribution were estimated by the linear combination of the probability weighted moments, L-moment. The regional and at-site analysis for the design rainfall were tested by Monte Carlo simulation. Relative root-mean-square error(RRMSE), relative bias(RBIAS) and relative reduction(RR) in RRMSE were computed and compared with those resulting from at-site Monte Carlo simulation. All show that the regional analysis procedure can substantially reduce the RRMSE, RBIAS and RR in RRMSE in the prediction of design rainfall. Consequently, optimal design rainfalls following the legions and consecutive durations were derived by the regional frequency analysis.

• Journal of the Korean Society of Safety
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• v.31 no.4
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• pp.48-54
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• 2016

The prediction of various emissions from coal combustion is an important subject of researchers and engineers because of environmental consideration. Therefore, the development of the models for predicting pollutants very fast has received much attention from international research community, especially in the field of safety assessment. In this work, response surface method was introduced as a design of experiment, and the database for RSM was set with the numerical simulation of a drop tube furnace (DTF) to predict the spatial distribution of pollutant concentrations as well as final ones. The distribution of carbon dioxide in DTF was assumed to have Boltzman function, and the resulted function with parameters of a high $R^2$ value facilitates predicting an accurate distribution of $CO_2$. However, CO distribution had a difference near peak concentration when Gaussian function was introduced to simulate the CO distribution. It might be mainly due to the anti-symmetry of the CO concentration in DTF, and hence Extreme function was used to permit the asymmetry. The application of Extreme function enhanced the regression accuracy of parameters and the prediction was in a fairly good agreement with the new experiments. These results promise the wide use of statistical models for the quantitative safety assessment.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.29 no.1
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• pp.62-66
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• 2017

The interest on the potential earthquake magnitude and the request on the earthquake-resistant design examination for coastal structures are emerged because of the recently occurred magnitude 5.8 earthquake in Gyeoung-Ju, Korea. In this study, the magnitude and its confidence intervals with the return periods are estimated using the KMA earthquake magnitude data (over 3.5 and 4.0 in magnitude) by the non-parametric extreme value analysis. In case of using the "over 4.0" data set, the estimated magnitudes on the 50- and 100-years return periods are 5.81 and 5.94, respectively. Their 90% confidence intervals are estimated to be 5.52-6.11, 5.62-6.29, respectively. Even though the estimated magnitudes have limitations not considering the spatial distribution, it can be used to check the stability of the diverse coastal structures in the perspective of the life design because the potential magnitude and its confidence intervals in Korea are estimated based on the available 38-years data by the extreme value analysis.

• 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.