• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.4
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• pp.151-161
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• 1993

The log-Gumbel distribution in real space is defined by transforming the conventional log-Gumbel distribution in log space. For this model, the parameter estimation techniques are applied based on the methods of moments, maximum likelihood and probability weighted moments. The asymptotic variances of estimator of the quantiles for each estimation method are derived to find the confidence limits for a given return period. Finally, the log-Gumbel model is applied to actual flood data to estimate the parameters, quantiles and confidence limits.

• 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.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.38 no.2
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• pp.249-259
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• 2018

More than half of annual rainfall occurs in summer season in Korea due to its climate condition and geographical location. A frequency analysis is mostly adopted for designing hydraulic structure under the such concentrated rainfall condition. Among the various distributions, univariate Gumbel distribution has been routinely used for rainfall frequency analysis in Korea. However, the distributional changes in extreme rainfall have been globally observed including Korea. More specifically, the univariate Gumbel distribution based rainfall frequency analysis is often fail to describe multimodal behaviors which are mainly influenced by distinct climate conditions during the wet season. In this context, we purposed a Gumbel mixture distribution based rainfall frequency analysis with a Bayesian framework, and further the results were compared to that of the univariate. It was found that the proposed model showed better performance in describing underlying distributions, leading to the lower Bayesian information criterion (BIC) values. The mixed Gumbel distribution was more robust for describing the upper tail of the distribution which playes a crucial role in estimating more reliable estimates of design rainfall uncertainty occurred by peak of upper tail than single Gumbel distribution. Therefore, it can be concluded that the mixed Gumbel distribution is more compatible for extreme frequency analysis rainfall data with two or more peaks on its distribution.

• 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.

• 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 Korea Water Resources Association
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• v.50 no.3
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• pp.211-221
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• 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.

• 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 Industrial Technology
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• v.35
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• pp.95-102
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• 2015

Two extreme wind speed prediction models, the EWM(Extreme wind speed model) in IEC61400-1 and the Gumbel method were compared in this study. The two models were used to predict extreme wind speeds of six different sites in Korea and the results were compared with long term wind data. The NCAR reanalysis data were used for inputs to two models. Various periods of input wind data were tried from 1 year to 50 years and the results were compared with the 50 year maximum wind speed of NCAR wind data. It was found that the EWM model underpredicted the extreme wind speed more than 5 % for two sites. Predictions from Gumbel method overpredicted the extreme wind speed or underpredicted it less than 5 % for all cases when the period of the input data is longer than 10 years. The period of the input wind data less than 3 years resulted in large prediction errors for Gumbel method. Predictions from the EWM model were not, however, much affected by the period of the input wind data.

• Journal of Korea Water Resources Association
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• v.52 no.11
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• pp.895-904
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• 2019

It has been well recognized that extreme rainfall process often features a nonstationary behavior, which may not be effectively modeled within a stationary frequency modeling framework. Moreover, extreme rainfall events are often described by a two (or more)-component mixture distribution which can be attributed to the distinct rainfall patterns associated with summer monsoons and tropical cyclones. In this perspective, this study explores a Mixture Distribution based Nonstationary Frequency (MDNF) model in a changing rainfall patterns within a Bayesian framework. Subsequently, the MDNF model can effectively account for the time-varying moments (e.g. location parameter) of the Gumbel distribution in a two (or more)-component mixture distribution. The performance of the MDNF model was evaluated by various statistical measures, compared with frequency model based on both stationary and nonstationary mixture distributions. A comparison of the results highlighted that the MDNF model substantially improved the overall performance, confirming the assumption that the extreme rainfall patterns might have a distinct nonstationarity.