• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.11 no.4
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• pp.460-466
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• 2018

With the development of information technology, the scale of computer software system is constantly expanding. Reliability and cost of software development have a great impact on software quality. In this study, based on the software failure interval time data, a comparative analysis was performed on the characteristics of the software development cost model based on the lifetime distribution following the Type-2 Gumbel and Erlang distribution in the NHPP model. As a result, the trends of the cost curves for the Go-Okumoto model and the proposed Erlang model and the Type-2 Gumble model both decreased in the initial stage and gradually increased in the latter half of the failure time. Also, Comparing the Erlang model with the Type-2 Gumble model, we found that the Erlang model is faster and more cost-effective at launch. Through this study, Software operators should remove possible defects from the testing phase rather than the operational phase to reduce defects after the software release date, it is expected to be able to study the prior information needed to understand the characteristic of software development cost.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.12 no.3
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• pp.211-217
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• 2019

In this study, we compare and analyze the attributes of the software development cost model according to the shape parameters change of the Type-2 Gumbel lifetime distribution using the NHPP model. In order to analyze the software failure phenomena, the parametric estimation is applied to the maximum likelihood estimation method, and the nonlinear equations are calculated using the bisection method. As a result, when the attributes of the cost curves according to the change of shape parameters are compared, it is found that the larger the number of shape parameters, the lower the software development cost and the faster the release time. Through this study, it is expected that it will be helpful for the software developers to search for the development cost according to the software shape parameters change, and also to provide the necessary information for the attributes of the software development cost.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.16 no.3
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• pp.130-141
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• 2004

For a coastal or harbor structure design, one of the most important environmental factors is the appropriate design wave condition. Especially, the information of deepwater wave height distribution is essential for reliability design. In this paper, a set of deep water wave data obtained from KORDI(2003) were analyzed for extreme wave heights. These wave data at 67 stations off the Korean coast from 1979 to 1998 were arranged in the 16 directions. The probability distributions considered in this research were the Weibull, the Gumbel, the Log-pearson Type-III, and Lognormal distribution. For each of these distributions, three parameter estimation methods, i.e. the method of moments, maximum likelihood and probability weighted moments, were applied. Chi-square and Kolmogorov-Smirnov goodness-of-fit tests were performed, and the assumed distribution was accepted at the confidence level 95%. Gumbel distribution which best fits to the 67 station was selected as the most probable parent distribution, and optimally estimated parameters and 50 year design wave heights were presented.

• Proceedings of the Korea Water Resources Association Conference
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• 2016.05a
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• pp.201-201
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• 2016

The asymptotic extreme value distributions of maxima are a natural choice when designing against future extreme events like flood peaks or wave heights, given a stationary time series. The generalized extreme value distribution (GEV) is often utilised in this context because it is seen as a convenient single expression for extreme event analysis. However, the GEV has a drawback because the location of the distribution bound relative to the data is a discontinuous function of the GEV shape parameter. That is, for annual maxima approximated by the Gumbel distribution, the data is also consistent with a GEV distribution with an upper bound (no lower bound) or a GEV distribution with a lower bound (no upper bound). A more consistent single extreme value expression for design purposes is proposed as the Weibull distribution of smallest extremes, as applied to transformed annual maxima. The Weibull distribution limit holds here for sufficiently large sample sizes, irrespective of the extreme value domain of attraction applicable to the untransformed maxima. The Gumbel, Type 2, and Type 3 extreme value distributions thus become redundant, together with the GEV, because in reality there is only a single asymptotic extreme value distribution required for design purposes - the Weibull distribution of minima as applied to transformed maxima. An illustrative synthetic example is given showing transformed maxima from the normal distribution approaching the Weibull limit much faster than the untransformed sample maxima approach the normal distribution Gumbel limit. Some New Zealand examples are given with the Weibull distribution being applied to reciprocal transformations of annual flood maxima, where the untransformed maxima follow apparently different extreme value distributions.

• Water for future
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• v.29 no.1
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• pp.129-139
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• 1996

It is very important to select appropriate distributions for hydrological data in planning and designing hydraulic structures. Also, it is necessary to check whether the selected distribution reproduces the statistical characteristics of the real data. In this study, the parameters of the two- and three-parameter gamma, two- and three-parameter lognormal, Gumbel, two- and three-parameter log-Gumbel, GEV, log-Pearsonn type III, two- and three-parameter Weibull, four- and five-parameter Wakeby distributions were estimated for the rainfall data of 22 sites in Korea with 7 different durations based on the methods of moments, probability weighted moments, and maximum likelihood. And the validity conditions were checked for the estimated parameters. The separation effect for each distribution was examined throught 10,000 simulations using the estimated parameters. As results, the separation effect was the smallest: log-Pearson type III for moment method, log-Pearson type III and GEV for probability weighted moment method, and GEV for maximum likelihood method. However, it is large for the two-parameter distributions.

• KCID journal
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• v.2 no.1
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• pp.20-29
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• 1995

It was attempted to get an optimal method for the prediction of design low flows among derivation . techniques of design low flows. Derivation techniques of design low Hon used in this study are Type III extremal, Gumbel-Chow distribution, SMEMAX(Small, M

• Journal of Wetlands Research
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• v.2 no.1
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• pp.49-58
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• 2000

The frequency analysis of annual maximum rainfall data and the derivation of probable rainfall intensity formula at Masan station are performed in this study. Based on the eight different rainfall duration data from 10 minutes to 24 hours, eight types of probability distribution (Gamma, Lognormal, Log-Pearson type III, GEV, Gumbel, Log-Gumbel, Weibull, and Wakeby distributions), three types of parameter estimation scheme (moment, maximum likelihood and probability weighted methods) and three types of goodness-of-fit test (${\chi}^2$, Kolmogorov-Smirnov and Cramer von Mises tests) were considered to find an appropriate probability distribution at Masan station. The Lognormal-2 distribution was selected and the probable rainfall intensity formula was derived by regression analysis. The derived formula can be used for estimating rainfall quantiles of the Masan vicinity areas with convenience and reliability in practice.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.29 no.1
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• pp.245-251
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• 2005

When we design coastal and harbol facilities deepwater design wave and wind speed are the important design parameters. Especially, the analysis of these informations is a vital step for the point of disaster prevention. In this study, we made and an extreme value analysis using a series of deep water significant wave data arranged in the 16 direction and supplied by KORDI real-time wave information system ,and the wind data gained from Wan-Do whether Station 1978-2003. The probability distributions considered in this characteristic analysis were the Weibull, the Gumbel, the Log-Pearson Type III, the Normal, the Lognormal, and the Gamma distribution. The parameter for each distribution was estimated by three methods, i.e. the method of moments, the maximum likelihood, and the method of probability weight moments. Furthermore, probability distributions for the extreme data had been selected by using Chi-square and Kolmogorov-Smirnov test within significant level of 5%, i,e. 95% reliance level. From this study we found that Gumbel distribution is the most proper model for the deep water design wave height off the southwest coast of Korea. However the result shows that the proper distribution made for the selected site is varied in each extreme data set.

• Journal of Korea Water Resources Association
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• v.55 no.6
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• pp.447-459
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• 2022

This study estimated the grid-type precipitation quantile for the Korean Peninsula using PERSIANN-CCS-CDR (Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Cloud Classification System-Climate Data Record), a satellite based re-analysis precipitation data. The period considered is a total of 38 years from 1983 to 2020. The spatial resolution of the data is 0.04° and the temporal resolution is 3 hours. For the probability distribution, the Gumbel distribution which is generally used for frequency analysis was used, and the probability weighted moment method was applied to estimate parameters. The duration ranged from 3 hours to 144 hours, and the return period from 2 years to 500 years was considered. The results were compared and reviewed with the estimated precipitation quantile using precipitation data from the Automated Synoptic Observing System (ASOS) weather station. As a result, the parameter estimates of the Gumbel distribution from the PERSIANN-CCS-CDR showed a similar pattern to the results of the ASOS as the duration increased, and the estimates of precipitation quantiles showed a rather large difference when the duration was short. However, when the duration was 18 h or longer, the difference decreased to less than about 20%. In addition, the difference between results of the South and North Korea was examined, it was confirmed that the location parameters among parameters of the Gumbel distribution was markedly different. As the duration increased, the precipitation quantile in North Korea was relatively smaller than those in South Korea, and it was 84% of that of South Korea for a duration of 3 h, and 70-75% of that of South Korea for a duration of 144 h.

• Journal of the Korean Society of Industry Convergence
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• v.2 no.1
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• pp.35-43
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• 1999

The purpose of this study is to derive the optimal methodology estimating the changes of fluvial hydraulic characteristics due to semi-covering work of urban stream. First, after collecting the data of the daily maximum rainfall of Chungju gaging station, the frequency analysis was carried out with frequency factor method, which includes normal, two-parameter and three-parameter lognormal, Gumbel-Chow, pearson type III, log-pearson type III distribution, and the goodness of fit test was executed by $x^2$-test and Kormogorov-Smimov test. Using the SCS method, the effective rainfall was estimated and the peak flow was calculated by the area-routing method. The HEC-2 model was applied to calculate water surface profiles for steady, gradually varied flow at Kyohyun river system in Chungju city. The model was applied to floodplain and riverbed management to evaluate flood way encroachments and to delineate flood hazard by riverside roadway construction. The model also was used to evaluate effects on water surface profiles of river improvement and levees as well as the presence of bridges or other hydraulic structures in the floodplain.