• Wind and Structures
• /
• v.25 no.3
• /
• pp.261-282
• /
• 2017

The probabilistic information of directional extreme wind speeds is important for precisely estimating the design wind loads on structures. A new joint probability distribution model of directional extreme wind speeds is established based on observed wind-speed data using multivariate extreme value theory with the t-Copula function in the present study. At first, the theoretical deficiencies of the Gaussian-Copula and Gumbel-Copula models proposed by previous researchers for the joint probability distribution of directional extreme wind speeds are analysed. Then, the t-Copula model is adopted to solve this deficiency. Next, these three types of Copula models are discussed and evaluated with Spearman's rho, the parametric bootstrap test and the selection criteria based on the empirical Copula. Finally, the extreme wind speeds for a given return period are predicted by the t-Copula model with observed wind-speed records from several areas and the influence of dependence among directional extreme wind speeds on the predicted results is discussed.

• The Korean Journal of Applied Statistics
• /
• v.24 no.3
• /
• pp.523-533
• /
• 2011

Most nancial preference methods for market risk management are to estimate VaR. In many real cases, it happens to obtain the VaRs of the univariate as well as multivariate distributions based on multivariate data. Copula functions are used to explore the dependence of non-normal random variables and generate the corresponding multivariate distribution functions in this work. We estimate Archimedian Copula functions including Clayton Copula, Gumbel Copula, Frank Copula that are tted to the multivariate earning rate distribution, and then obtain their VaRs. With these Copula functions, we estimate the VaRs of both a certain integrated industry and individual industries. The parameters of three kinds of Copula functions are estimated for an illustrated stock data of two Korean industries to obtain the VaR of the bivariate distribution and those of the corresponding univariate distributions. These VaRs are compared with those obtained from other methods to discuss the accuracy of the estimations.

• Computers and Concrete
• /
• v.21 no.2
• /
• pp.181-187
• /
• 2018

In order to solve the life prediction problem of damaged coating steel bar in magnesium cement concrete, this study tries to establish the marginal distribution function by using the corrosion current density as a single degradation factor. Representing the degree of steel corrosion, the corrosion current density were tested in electrochemical workstation. Then based on the Copula function, the joint distribution function of the damaged coating was established. Therefore, it is indicated that the corrosion current density of the bare steel and coated steel bar can be used as the boundary element to establish the marginal distribution function. By using the Frank-Copula function of Copula Archimedean function family, the joint distribution function of the damaged coating steel bar was successfully established. Finally, the life of the damaged coating steel bar has been lost in 7320d. As a new method for the corrosion of steel bar under the multi-dimensional factors, the two-dimensional Copula function has certain practical significance by putting forward some new ideas.

• Geomechanics and Engineering
• /
• v.36 no.6
• /
• pp.601-618
• /
• 2024

The joint probability distribution of uncertain geomechanical parameters of geotechnical strata is a crucial aspect in constructing the reliability functional function for roof structures. However, due to the limited number of on-site exploration and test data samples, it is challenging to conduct a scientifically reliable analysis of roof geotechnical strata. This study proposes a Copula method based on small sample exploration and test data to construct the intensity characteristics of roof geotechnical strata. Firstly, the theory of multidimensional copula is systematically introduced, especially the construction of four-dimensional Gaussian copula. Secondly, data from measurements of 176 groups of geomechanical parameters of roof geotechnical strata in 31 coal mines in China are collected. The goodness of fit and simulation error of the four-dimensional Gaussian Copula constructed using the Pearson method, Kendall method, and Spearman methods are analyzed. Finally, the fitting effects of positive and negative correlation coefficients under different copula functions are discussed respectively. The results demonstrate that the established multidimensional Gaussian Copula joint distribution model can scientifically represent the uncertainty of geomechanical parameters in roof geotechnical strata. It provides an important theoretical basis for the study of reliability functional functions for roof structures. Different construction methods for multidimensional Gaussian Copula yield varying simulation effects. The Kendall method exhibits the best fit in constructing correlations of geotechnical parameters. For the bivariate Copula fitting ability of uncertain parameters in roof geotechnical strata, when the correlation is strong, Gaussian Copula demonstrates the best fit, and other Copula functions also show remarkable fitting ability in the region of fixed correlation parameters. The research results can offer valuable reference for the stability analysis of roof geotechnical engineering.

• Journal of Korea Water Resources Association
• /
• v.45 no.8
• /
• pp.827-837
• /
• 2012

The estimation of the rainfall quantile is of great importance in designing hydrologic structures. Conventionally, the rainfall quantile is estimated by univariate frequency analysis with an appropriate probability distribution. There is a limitation in which duration of rainfall is restrictive. To overcome this limitation, bivariate frequency analysis by using 3 copula models is performed in this study. Annual maximum rainfall events in 5 stations are used for frequency analysis and rainfall depth and duration are used as random variables. Gumbel (GUM), generalized logistic (GLO) distributions are applied for rainfall depth and generalized extreme value (GEV), GUM, GLO distributions are applied for rainfall duration. Copula models used in this study are Frank, Joe, and Gumbel-Hougaard models. Maximum pseudo-likelihood estimation method is used to estimate the parameter of copula, and the method of probability weighted moments is used to estimate the parameters of marginal distributions. Rainfall quantile from this procedure is compared with various marginal distributions and copula models. As a result, in change of marginal distribution, distribution of duration does not significantly affect on rainfall quantile. There are slight differences depending on the distribution of rainfall depth. In the case which the marginal distribution of rainfall depth is GUM, there is more significantly increasing along the return period than GLO. Comparing with rainfall quantiles from each copula model, Joe and Gumbel-Hougaard models show similar trend while Frank model shows rapidly increasing trend with increment of return period.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.15 no.5
• /
• pp.2603-2609
• /
• 2014

Reliability analysis of mechanical systems requires statistical modeling of input random variables such as distribution function types and statistical parameters that affect the performance of the mechanical systems. Some random variables are correlated, but considered as independent variables or wrong assumptions on input random variables have been used. In this paper, joint distributions were modeled using copulas and Bayesian method from limited number of data. To verify the proposed method, statistical simulation tests were carried out for various number of samples and correlation coefficients. As a result, the Bayesian method selected the most probable copula types among candidate copulas even though the candidate copula shapes are similar for low correlations or the number of data is limited. The most probable copulas also yielded similar reliabilities with the true reliability obtained from a true copula, so that it can be concluded that the Bayesian method provides accurate statistical modeling for the reliability analysis.

• IE interfaces
• /
• v.24 no.1
• /
• pp.24-39
• /
• 2011

In this paper, we study the methodology for the measurement and integration of market risk and credit risk using Copula. We apply the methodology of Rosenberg, and Schuermann(2006) to the assets of pension system. Firstly we estimate dynamics of risk factors and their effects on investment returns, then use the estimated result to simulate future movement of risk factors and distribution of investment returns. Finally we measure integrated risk using integrated return distribution by Copula and simulated future investment return distributions. We found the integrated risk changing with the correlation of risks and investment weights of risks and confirmed the diversification effect of risks. This result is consistent when we use normal Copula and normal marginals, t-Copula and t(3) marginals, and normal Copula and non-parametric marginals. And in the case of non-parametric maginals, larger integrated risk is calculated. It means that use of non-parametric marginals is more conservative.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.2
• /
• pp.421-433
• /
• 2017

The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. Hong et al. (2016) proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2019.05a
• /
• pp.151-151
• /
• 2019

Because drought is a complex and stochastic phenomenon in nature, statistical approaches for drought assessment receive great attention for water resource planning and management. Generally drought characteristics such as severity, duration and intensity are modelled separately. This study aims to develop a relationship between drought characteristics using a bivariate copula model. To achieve the objective, we calculated the Standardized Precipitation Index (SPI) using rainfall data at 6 rain gauge stations for the period of 1961-1999 in Jehlum River Basin, Pakistan, and investigated the drought characteristics. Since there is a significant correlation between drought severity and duration, they are usually modeled using different marginal distributions and joint distribution function. Using exponential distribution for drought severity and log-logistic distribution for drought duration, the Galambos copula was recognized as best copula to model joint distribution of drought severity and duration based on the KS-statistic. Various return periods of drought were calculated to identify time interval of repeated drought events. The result of this study can provide useful information for effective water resource management and shows superiority against univariate drought analysis.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.32 no.3B
• /
• pp.161-168
• /
• 2012

Drought is a normal and recurrent phenomenon. But, recurring prolonged droughts have caused consequences and diverse impacts on human system. Therefore, understanding drought characteristics is indispensable element in well-prepared drought management. This study aims to investigate the hydrological droughts of Pyongchang stream and Upstream of Namhan-river in Korean peninsula. For modelling of the joint distribution of drought duration and drought severity, the copula method is used to construct the bivariate drought distribution and return period from the predetermined marginal distributions of drought duration and drought severity. As the result, the most severed drought of the Pyongchang stream and Upstream of Namhan-river occuring during period 1967 to 2007 is the 1981 and 1973. Return period for this drought derived from copula is 550 and 110 years.