• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.481-504
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• 2006

VaR, a tail-related risk measure is now widely used as a tool for a measurement and a management of financial risks. For more accurate measurement of VaR, recently we are particularly concerned about the approach based on extreme value theory rather than the traditional method based on the assumption of normal distribution. However, many studies about the approaches using extreme value theory was done only for the univariate case. In this paper, we discuss portfolio risk measurements with modelling multivariate extreme value distributions by combining copulas and extreme value theory. We also discuss the estimation of ES together with VaR as portfolio risk measures. Finally, we investigate the relative superiority of EVT-copula approach than variance-covariance method through the back-testing of an empirical data.

• Knowledge Management Research
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• v.22 no.2
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• pp.247-268
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• 2021

Investors mainly use PER and PBR among financial ratios for valuation and investment decision-making. I conduct an analysis of two basic financial ratios from a statistical perspective. Financial ratios contain key accounting numbers which reflect firm fundamentals and are useful for valuation or risk analysis such as enterprise credit evaluation and default prediction. The distribution of financial data tends to be extremely heavy-tailed, and PER and PBR show exceedingly high level of kurtosis and their extreme cases often contain significant information on financial risk. In this respect, Extreme Value Theory is required to fit its right tail more precisely. I introduce not only GPD but exGPD. GPD is conventionally preferred model in Extreme Value Theory and exGPD is log-transformed distribution of GPD. exGPD has recently proposed as an alternative of GPD(Lee and Kim, 2019). First, I conduct a simulation for comparing performances of the two distributions using the goodness of fit measures and the estimation of 90-99% percentiles. I also conduct an empirical analysis of Information Technology firms in Korea. Finally, exGPD shows better performance especially for PBR, suggesting that exGPD could be an alternative for GPD for the analysis of financial ratios.

• Journal of the Korean Data and Information Science Society
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• v.20 no.4
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• pp.705-712
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• 2009

Histogram is the oldest and most widely used density estimator for presentation and exploration of observed univariate data. The structure of a histogram really depends on the number of bins and the width of the bins, so that slight changes on bins can produce totally different shape of a histogram. In order to solve this problem the fuzzy histogram was introduced and the result was good enough (Loquin and Strauss, 2008). In particular, when estimating loss distribution related with operational risk a histogram has been widely used. In this article, instead of an ordinary histogram we try to use a fuzzy histogram for estimating loss distribution and show that a fuzzy histogram provide more stable results.

• Journal of the Korean Data and Information Science Society
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• v.28 no.6
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• pp.1415-1425
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• 2017

Typhoons are accompanied by strong wind and heavy rains. It causes casualties and property damage on the Korean peninsula every year. The effect of typhoon to daily precipitation should be quantified to prevent the damage of typhoon. Daily precipitation, maximum wind speed and, mean wind speed data was collected from 60 weather stations between 1976 and 2016. The parameters of the generalized extreme value distribution were estimated through the maximum likelihood estimation and the L-moment estimation. The impact of a typhoon can be obtained through a comparison of return levels between the whole data and typhoon excluded data. We conclude that the eastern and southern coastline are exposed to the risk of heavy rainfall which is caused by typhoon.

• Journal of the Korean Data and Information Science Society
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• v.28 no.4
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• pp.797-810
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• 2017

The Korean peninsula is exposed to typhoons every year. Typhoons cause huge socioeconomic damage because tropical cyclones tend to occur with strong winds and heavy precipitation. In order to understand the complex dependence structure between strong winds and heavy precipitation, the copula links a set of univariate distributions to a multivariate distribution and has been actively studied in the field of hydrology. In this study, we carried out analysis using data of wind speed and precipitation collected from the weather stations in Busan and Jeju. Log-Normal, Gamma, and Weibull distributions were considered to explain marginal distributions of the copula. Kolmogorov-Smirnov, Cramer-von-Mises, and Anderson-Darling test statistics were employed for testing the goodness-of-fit of marginal distribution. Observed pseudo data were calculated through inverse transformation method for establishing the copula. Elliptical, archimedean, and extreme copula were considered to explain the dependence structure between strong winds and heavy precipitation. In selecting the best copula, we employed the Cramer-von-Mises test and cross-validation. In Busan, precipitation according to average wind speed followed t copula and precipitation just as maximum wind speed adopted Clayton copula. In Jeju, precipitation according to maximum wind speed complied Normal copula and average wind speed as stated in precipitation followed Frank copula and maximum wind speed according to precipitation observed Husler-Reiss copula.

• Journal of Digital Convergence
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• v.14 no.7
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• pp.309-319
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• 2016

There is a need to develop a data quality management algorithm in order to improve the quality of health care data. In this study, we developed a data quality control algorithms associated diseases related to diabetes in patients with hypertension. To make a data quality algorithm, we extracted hypertension patients from 2011 and 2012 discharge damage survey data. As the result of developing Data quality management algorithm, significant factors in hypertension patients with diabetes are gender, age, Glomerular disorders in diabetes mellitus, Diabetic retinopathy, Diabetic polyneuropathy, Closed [percutaneous] [needle] biopsy of kidney. Depending on the decision tree results, we defined Outlier which was probability values associated with a patient having diabetes corporal with hypertension or more than 80%, or not more than 20%, and found six groups with extreme values for diabetes accompanying hypertension patients. Thus there is a need to check the actual data contained in the Outlier(extreme value) groups to improve the quality of the data.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.101-114
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• 2012

In car insurance, the loss ratio is the ratio of total losses paid out in claims divided by the total earned premiums. In order to minimize the loss to the insurance company, estimating extreme quantiles of loss ratio distribution is necessary because the loss ratio has essential prot and loss information. Like other types of insurance related datasets, the distribution of the loss ratio has heavy-tailed distribution. The Peaks over Threshold(POT) and the Hill estimator are commonly used to estimate extreme quantiles for heavy-tailed distribution. This article compares and analyzes the performances of various kinds of parameter estimating methods by using a simulation and the real loss ratio of car insurance data. In addition, we estimate extreme quantiles using the Hill estimator. As a result, the simulation and the loss ratio data applications demonstrate that the POT method estimates quantiles more accurately than the Hill estimation method in most cases. Moreover, MLE, Zhang, NLS-2 methods show the best performances among the methods of the GPD parameters estimation.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.1001-1012
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• 2016

It is well known that air pollutants exert a bad influence on human health. According to the United Nations Environment Program, 4.3 million people die from carbon monoxide and particulate matter annually from all over the world. Carbon monoxide is a toxic gas that is the most dangerous of the gas consisting of carbon and oxygen. In this paper, we used 1 hour, 6 hours, 12 hours, and 24 hours average carbon monoxide concentration data collected between 2004 and 2013 in Daegu Gyeongbuk area. Parameters of the generalized extreme value distribution were estimated by maximum likelihood estimation and L-moments estimation. An evalution of goodness of fitness also was performed. Since the number of samples were small, L-moment estimation turned out to be suitable for parameter estimation. We also calculated 5 year, 10 year, 20 year, and 40 year return level.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.833-845
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• 2011

This paper conducts a statistical analysis of extreme values for both daily log-returns and daily negative log-returns, which are computed using a collection of KOSPI data from January 3, 1998 to August 31, 2011. The Poisson-GPD model is used as a statistical analysis model for extreme values and the maximum likelihood method is applied for the estimation of parameters and extreme quantiles. To the Poisson-GPD model is also added the Bayesian method that assumes the usual noninformative prior distribution for the parameters, where the Markov chain Monte Carlo method is applied for the estimation of parameters and extreme quantiles. According to this analysis, both the maximum likelihood method and the Bayesian method form the same conclusion that the distribution of the log-returns has a shorter right tail than the normal distribution, but that the distribution of the negative log-returns has a heavier right tail than the normal distribution. An advantage of using the Bayesian method in extreme value analysis is that there is nothing to worry about the classical asymptotic properties of the maximum likelihood estimators even when the regularity conditions are not satisfied, and that in prediction it is effective to reflect the uncertainties from both the parameters and a future observation.

• Journal of Digital Convergence
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• v.18 no.10
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• pp.33-39
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• 2020

In order to cope with traffic accidents efficiently, the maximum number of traffic accidents, deaths and serious injuries that can occur during the day should be presented quantitatively. In order to examine the characteristics of traffic accidents in different regions, it was divided into the Seoul metropolitan area, Chungcheong area, Gyeongbuk area, Honam area, and Gyeongnam area and was suitable for the generalized extreme value distribution (GEV). The parameters of the GEV distribution were estimated by the L-moments, and the Anderson-Darling test and the Cramer-von Mises test confirmed the suitability of the distribution. According to the analysis, the maximum number of traffic accidents that can occur once every 50 years is 401 in the Seoul metropolitan area, 168 in the South Gyeongsang region, 455 in the North Gyeongsang region, 136 in the Chungcheong region and 205 in the South Jeolla region. Compared to the Seoul metropolitan area, which has a large population and car registration, the number of traffic accidents is relatively high due to the large area, mountainous areas, and logistics movement caused by the industrial complex.