• Journal of the Korean Data and Information Science Society
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• v.27 no.6
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• pp.1453-1463
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• 2016

The most useful financial risk measure may be VaR (Value at Risk) which estimates the maximum loss amount statistically. The VaR tends to be estimated in many industries by using transformed univariate risk including variance-covariance matrix and a specific portfolio. Hong et al. (2016) are defined the Vector at Risk based on the multivariate quantile vector. When a specific portfolio is given, one point among Vector at Risk is founded as the best VaR which is called as an alternative VaR (AVaR). In this work, AVaRs have been investigated for multivariate normal distributions with many kinds of variance-covariance matrix and various portfolio weight vectors, and compared with VaRs. It has been found that the AVaR has smaller values than VaR. Some properties of AVaR are derived and discussed with these characteristics.

• Journal of the Korean Data and Information Science Society
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• v.28 no.5
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• pp.959-970
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• 2017

In this study, we propose bivariate skewness and kurtosis statistics and suggest a surface plot that can visually implement bivariate data containing the correlation coefficient. The skewness statistic is expressed in the form of a paired real values because this represents the skewed directions and degrees of the bivariate random sample. The kurtosis has a positive value which can determine how thick the tail part of the data is compared to the bivariate normal distribution. Moreover, the surface plot implements bivariate data based on the quantile vectors. Skewness and kurtosis are obtained and surface plots are explored for various types of bivariate data. With these results, it has been found that the values of the skewness and kurtosis reflect the characteristics of the bivariate data implemented by the surface plots. Therefore, the skewness, kurtosis and surface plot proposed in this paper could be used as one of valuable descriptive statistical methods for analyzing bivariate distributions.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.87-98
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• 2017

The multivaiate empirical distribution function (MEDF) is defined in this work. The MEDF's expectation and variance are derived and we have shown the MEDF converges to its real distribution function. Based on random samples from bivariate standard normal distribution with various correlation coefficients, we also obtain MEDFs and propose two kinds of graphical methods to visualize MEDFs on two dimensional plane. One is represented with at most n stairs with similar arguments as the step function, and the other is described with at most n curves which look like bivariate quantile vector. Even though these two descriptive methods could be expressed with three dimensional space, two dimensional representation is obtained with ease and it is enough to explain characteristics of bivariate distribution functions. Hence, it is possible to visualize trivariate empirical distribution functions with three dimensional quantile vectors. With bivariate and four variate illustrative examples, the proposed MEDFs descriptive plots are obtained and explored.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.119-130
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• 2017

In many literatures on VaR and CTE for multivariate distribution, these are estimated by using transformed univariate distribution with a specific ratio of many kinds of portfolios. Even though there are lots of works to define quantiles for multivariate distributions, there does not exist a quantile uniquely. Hence, it is not easy to define the VaR and CTE. In this paper, we propose the weighted CTE vectors corresponding to various ratio combinations of many kinds of portfolios by extending the researches on the alternative VaR and integrated multivariate CTE based on multivariate quantiles. We extend relation equations about univariate CTEs to multivariate CTE vectors and discuss their characteristics. The proposed weighted CTEs are explored with some data from multivariate normal distribution and illustrative examples.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1201-1212
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• 2016

Value at Risk (VaR) for market risk management is a favorite method used by financial companies; however, there are some problems that cannot be explained for the amount of loss when a specific investment fails. Conditional Tail Expectation (CTE) is an alternative risk measure defined as the conditional expectation exceeded VaR. Multivariate loss rates are transformed into a univariate distribution in real financial markets in order to obtain CTE for some portfolio as well as to estimate CTE. We propose multivariate CTEs using multivariate quantile vectors. A relationship among multivariate CTEs is also derived by extending univariate CTEs. Multivariate CTEs are obtained from bivariate and trivariate normal distributions; in addition, relationships among multivariate CTEs are also explored. We then discuss the extensibility to high dimension as well as illustrate some examples. Multivariate CTEs (using variance-covariance matrix and multivariate quantile vector) are found to have smaller values than CTEs transformed to univariate. Therefore, it can be concluded that the proposed multivariate CTEs provides smaller estimates that represent less risk than others and that a drastic investment using this CTE is also possible when a diversified investment strategy includes many companies in a portfolio.

• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.579-590
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• 2017

The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.689-697
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• 2016

The most useful method for financial market risk management may be Value at Risk (VaR) which estimates the maximum loss amount statistically. The VaR is used as a risk measure for one industry. Many real cases estimate VaRs for many industries or nationwide industries; consequently, it is necessary to estimate the VaR for multivariate distributions when a specific portfolio is established. In this paper, the multivariate quantile vector is proposed to estimate VaR for multivariate distribution, and the Vector at Risk for multivariate space is defined based on the quantile vector. When a weight vector for a specific portfolio is given, one point among Vector at Risk could be found as the best VaR which is called as an alternative VaR. The alternative VaR proposed in this work is compared with the VaR of Morgan with bivariate and trivariate examples; in addition, some properties of the alternative VaR are also explored.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.239-239
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• 2023

최근 도시화 및 기후변화에 따른 재난의 피해가 증가하고 있다. 국내 기상청에서는 호우 및 태풍에 대한 예·경보(주의보, 경보)를 전국적으로 통일된 기준(3시간, 12시간 누적강우량)에 따라 발령하고 있다. 이에 따라 현재 예·경보 기준에는 피해가 발생한 사상에 대한 지역별 특성이 고려되지 않는 문제점이 있다. 본 연구에서는 이러한 문제점을 해결하기 위하여 서울특별시, 인천광역시, 경기도의 호우 및 태풍에 대한 재해사상별 발생한 피해액 및 누적강우량을 활용하여 재해강도의 단계별 기준을 수립하고, 입력자료로 관측된 강우값을 활용하여 발생할 수 있는 재해의 발생 강도를 분류하는 모형을 개발하고자 하였다. 본 연구에서는 호우 및 태풍에 의한 재해 피해액의 분위별로 재해강도 단계(관심, 주의, 경계, 심각)를 분류하였고, 재해강도 단계에 따른 누적강우량 기준을 지자체별로 제시하였으며, 분류한 재해의 강도 단계를 모형의 종속변수로 활용하였다. 재해피해가 발생하지 않은 무강우 지속시간을 산정하여 호우 사상을 분류하였다. 지자체별로 재해 발생강도 분류 모형 개발을 위하여 머신러닝 모형 4가지(의사결정나무, 서포트 벡터 머신, 랜덤 포레스트, XGBoost)를 활용하였다. 본 연구에서 분류한 피해가 발생하지 않은 호우사상 및 피해가 발생한 사상별로 강우량, 지속시간 최대 강우량(3시간, 12시간), 선행강우량, 누적강우량을 독립변수로 입력하여 종속변수인 재해 발생 강도를 분류하였다. 각 모형별로 F1 Score를 이용한 정확도 평가 결과, 의사결정나무의 F1 Score가 평균 0.56으로 가장 우수한 정확도를 가지는 것으로 평가되었다. 본 연구에서 제시하는 머신러닝 기반 재해 발생 강도 분류모형을 활용하면 호우 및 태풍에 의한 재해에 대하여 지자체별로 재해 발생 강도를 단계별로 파악할 수 있어, 재난 담당자들의 의사결정을 위한 참고 자료로 활용될 수 있을 것으로 판단된다.

• Journal of Korea Water Resources Association
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• v.56 no.4
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• pp.261-272
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• 2023

In recent years, natural disasters such as heavy rainfall and typhoons have occurred more frequently, and their severity has increased due to climate change. The Korea Meteorological Administration (KMA) currently uses the same criteria for all regions in Korea for watch and warning based on the maximum cumulative rainfall with durations of 3-hour and 12-hour to reduce damage. However, KMA's criteria do not consider the regional characteristics of damages caused by heavy rainfall and typhoon events. In this regard, it is necessary to develop new criteria considering regional characteristics of damage and cumulative rainfalls in durations, establishing four stages: blue, yellow, orange, and red. A classification model, called DSCM (Disaster Severity Classification Model), for the four-stage disaster severity was developed using four machine learning models (Decision Tree, Support Vector Machine, Random Forest, and XGBoost). This study applied DSCM to local governments of Seoul, Incheon, and Gyeonggi Province province. To develop DSCM, we used data on rainfall, cumulative rainfall, maximum rainfalls for durations of 3-hour and 12-hour, and antecedent rainfall as independent variables, and a 4-class damage scale for heavy rain damage and typhoon damage for each local government as dependent variables. As a result, the Decision Tree model had the highest accuracy with an F1-Score of 0.56. We believe that this developed DSCM can help identify disaster risk at each stage and contribute to reducing damage through efficient disaster management for local governments based on specific events.