• Journal of Korean Society of Steel Construction
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• v.22 no.6
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• pp.573-580
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• 2010

In this study, an assessment method that considers the effects of directional wind speeds on buildings or structures that are sensitive to wind is proposed. Also, the basic characteristics of directional wind speeds were assessed by means of local annual maximum wind speeds. From the method of assessment of the characteristics of directional wind speeds, their goodness-of-fit was verified by applying extreme value distribution to the data on annual maximum wind speeds from the Korea Meteorological Administration. To consider the characteristics of directional winds, an assessment method is suggested that divides the directional wind pattern of each directional wind speed into four groups. From the study results, all the data on directional wind speeds based on the Gumbel distribution were examined using data on annual maximum wind speeds from Seoul, Tongyung, and Incheon. Since the Gumbel model of all directional wind speeds has independent probability characteristics that govern the 4 directional wind pattern groups, the application ratio proposed was based on the assessment of these four groups. According to the goodness-of-fit of the data on the annual maximum wind speeds based on the Gumbel distribution, new application ratios were proposed that consider the directional wind speeds in Seoul, Tongyung, and Incheon.

• Journal of Korea Water Resources Association
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• v.48 no.5
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• pp.331-343
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• 2015

Most nonstationary frequency models are defined as the probability models containing the time-dependent parameters. For frequency analysis of annual maximum rainfall data, the Gumbel distribution is generally recommended in Korea. For the nonstationary Gumbel models, the time-dependent location and scale parameters are defined as linear and exponential relationship, respectively. The exponentially time-varying scale parameter of nonstationary Gumbel model is generally used because the scale parameter should be positive. However, the exponential form of scale parameter occasionally provides overestimated quantiles. In this study, various forms of time-varying scale parameters such as exponential, linear, and logarithmic forms were proposed and compared. The parameters were estimated based on the method of maximum likelihood. To compare the accuracy of each scale parameter, Monte Carlo simulation was performed for various conditions. Additionally, nonstationary frequency analysis was conducted for the sites which have more than 30 years data with a trend in rainfall data. As a result, nonstationary Gumbel model with exponentially time-varying scale parameter generally has the smallest root mean square error comparing with another forms.

• Wind and Structures
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• v.26 no.6
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• pp.383-395
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• 2018

An accurate determination of wind speed distribution is the basis for an evaluation of the wind energy potential required to design a wind turbine, so it is important to estimate unknown parameters of wind speed distribution. In this paper, Gumbel distribution is used in modelling wind speed data, and alternative robust estimation methods to estimate its parameters are considered. The methodologies used to obtain the estimators of the parameters are least absolute deviation, weighted least absolute deviation, median/MAD and least median of squares. The performances of the estimators are compared with traditional estimation methods (i.e., maximum likelihood and least squares) according to bias, mean square deviation and total mean square deviation criteria using a Monte-Carlo simulation study for the data with and without outliers. The simulation results show that least median of squares and median/MAD estimators are more efficient than others for data with outliers in many cases. However, median/MAD estimator is not consistent for location parameter of Gumbel distribution in all cases. In real data application, it is firstly demonstrated that Gumbel distribution fits the daily mean wind speed data well and is also better one to model the data than Weibull distribution with respect to the root mean square error and coefficient of determination criteria. Next, the wind data modified by outliers is analysed to show the performance of the proposed estimators by using numerical and graphical methods.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.405-416
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• 2013

This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.

• Journal of Korea Water Resources Association
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• v.39 no.8 s.169
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• pp.659-668
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• 2006

The uncertainty of the risk of failure of hydraulic structures can be determined by estimating the variance of the risk of failure based on the methods of moments, probability weighted moments, and maximum likelihood assuming that the underlying model is the Gumbel distribution. In this paper, the variance of the risk of failure was derived. Monte Carlo simulation was peformed to verify the characteristics of the derived formulas for various sample size, design life, nonexceedance probability, and variation coefficient. As the results, PWM showed the smallest relative bias and root mean square error than the others while ML showed the smallest ones for relatively large sample siBes regardless of design life and nonexceedance probability. Also, it was found that variation coefficient does not effect on the relative bias and relative root mean square error.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.4B
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• pp.389-397
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• 2010

This study introduced a Bayesian based frequency analysis in which the statistical trend analysis for hydrologic extreme series is incorporated. The proposed model employed Gumbel extreme distribution to characterize extreme events and a fully coupled bayesian frequency model was finally utilized to estimate design rainfalls in Seoul. Posterior distributions of the model parameters in both Gumbel distribution and trend analysis were updated through Markov Chain Monte Carlo Simulation mainly utilizing Gibbs sampler. This study proposed a way to make use of nonstationary frequency model for dynamic risk analysis, and showed an increase of hydrologic risk with time varying probability density functions. The proposed study showed advantage in assessing statistical significance of parameters associated with trend analysis through statistical inference utilizing derived posterior distributions.

• Communications for Statistical Applications and Methods
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• v.30 no.5
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• pp.467-483
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• 2023

In this research, a conversion function and a distortion associated with the conversion function are defined and used to derive a unit power Gompertz distortion. A new family of copulas is built using the global distorted function. Four base copulas, namely Clayton, Gumbel, Frank, and Gaussian, are distorted into the family. Some properties including tail dependence coefficients and tail order are examined. Kendall's tau formula is derived for new copulas when the base copula is Clayton, Gumbel, or Frank. The maximum pseudo-likelihood estimation method is employed, and a simulation study was performed. The log-likelihood and AIC are reported to compare the performance of the fitted copulas. According to the applied data, the results indicate that new distorted copulas with additional parameters improve the fit.

• Proceedings of the Korea Water Resources Association Conference
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• 2010.05a
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• pp.581-585
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• 2010

This study introduced a Bayesian based frequency analysis in which the statistical trend seasonal analysis for hydrologic extreme series is incorporated. The proposed model employed Gumbel and GEV extreme distribution to characterize extreme events and a fully coupled bayesian frequency model was finally utilized to estimate design rainfalls in Seoul. Posterior distributions of the model parameters in both trend and seasonal analysis were updated through Markov Chain Monte Carlo Simulation mainly utilizing Gibbs sampler. This study proposed a way to make use of nonstationary frequency model for dynamic risk analysis, and showed an increase of hydrologic risk with time varying probability density functions. In addition, full annual cycle of the design rainfall through seasonal model could be applied to annual control such as dam operation, flood control, irrigation water management, and so on. The proposed study showed advantage in assessing statistical significance of parameters associated with trend analysis through statistical inference utilizing derived posterior distributions.

• Communications for Statistical Applications and Methods
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• v.29 no.4
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• pp.403-411
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• 2022

This article presents an independence test between pairs of interval censored failure times. The Mantel-Haenszel test is commonly applied to test the independence between two categorical variables accompanied with a strata variable. Hsu and Prentice (1996) applied a Mantel-Haenszel test to the sequence of 2 × 2 tables formed at the grids which are composed of failure times. In this article, due to unknown failure times, the suitable grid points should be determined and the status of failure and at risk are estimated at those grid points. We also consider a weighted test statistic to bring a more powerful test. Simulation studies are performed to evaluate the power of test statistics under finite samples. The method is applied to analyze two real data sets, mastitis data from milk cows and an age-related eye disease study.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.26 no.1
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• pp.16-24
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• 2014

Long-term measured wind data are absolutely necessary to estimate extreme offshore wind speed. However, it is almost impossible to collect offshore wind measured data. Therefore, typhoon simulation is widely used to analyze offshore wind conditions. In this paper, 74 typhoons which affected the western sea of Korea during 1978-2012(35 years) were simulated using Holland(1980) model. The results showed that 49.02 m/s maximum wind speed affected by BOLAVEN(1215) at 100 m heights of HeMOSU-1 (Herald of Meteorological and Oceanographic Special Unit - 1) was the biggest wind speed for 35 years. Meanwhile, estimated wind speeds were compared with observed data for MUIFA, BOLAVEN, SANBA at HeMOSU-1. And to estimate extreme wind speed having return periods, extreme analysis was conducted by assuming 35 annual maximum wind speed at four site(HeMOSU-1, Gunsan, Mokpo and Jeju) in western sea of the Korean Peninsular to be Gumbel distribution. As a results, extreme wind speed having 50-year return period was 50 m/s, that of 100-year was 54.92 m/s at 100 m heights, respectively. The maximum wind speed by BOLAVEN could be considered as a extreme winds having 50-year return period.